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705-805 (Hard)|   Geometry|      
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In the figure AB and CD are two diameters of circle. Interse Updated on: 04 Dec 2014, 04:32
Originally posted by PathFinder007 on 03 Aug 2014, 02:28.
Last edited by Bunuel on 04 Dec 2014, 04:32, edited 1 time in total.
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In the figure AB and CD are two diameters of circle. Intersecting at angle 48 degree. E is any point on Arc CB. find angle CEB

A. 114
B. 100
C. 80
D. 96
E. 40
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A
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In the figure AB and CD are two diameters of circle. Interse 04 Aug 2014, 06:39
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Since, CD and AB are two diameters of the circle, so their intersection is the centre. Let's denote this centre O. Angle CEB is inscribed, and angle COB is corresponding central angle (arc CAB). The value of angle COB=180+48=228 degrees. The measure of inscribed angle is always half the measure of the central angle. Angle CEB is equal =228/2=114 degrees.

The correct answer is A.


Hi,

I thought angle COB is 180-42=138 degrees. You have derived angle COB of 228 degrees.
Can you please explain.
Show more

That's why I mentioned arc CAB. You don't really need to understand the notions of major and minor arc. Corresponding central angle means that it stays on the same arc as your inscribed angle.
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In the figure AB and CD are two diameters of circle. Interse 03 Aug 2014, 02:37
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Since, CD and AB are two diameters of the circle, so their intersection is the centre. Let's denote this centre O. Angle CEB is inscribed, and angle COB is corresponding central angle (arc CAB). The value of angle COB=180+48=228 degrees. The measure of inscribed angle is always half the measure of the central angle. Angle CEB is equal =228/2=114 degrees.

The correct answer is A.
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In the figure AB and CD are two diameters of circle. Interse 12 Nov 2018, 09:17
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In the figure AB and CD are two diameters of circle. Intersecting at angle 48 degree. E is any point on Arc CB. find angle CEB

A. 114
B. 100
C. 80
D. 96
E. 40
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Let's use some useful circle properties

First let's add a blue line, to divide ∠CEB into 2 angles



CD is the DIAMETER of the circle
Since ∠CED is an inscribed angle containing (aka "holding") the diameter, we can conclude that ∠CED = 90°



Now recognize that the intersection of AB and CD creates two equal (vertically opposite) angles, we can conclude the angle opposite the 48° is also 48°



Now recognize that we have two angles containing (aka "holding") the arc BD
Property: If a CENTRAL angle and an INSCRIBED angle contain the same arc, then the CENTRAL angle is TWICE the INSCRIBED angle
This means that ∠DEB = 24°


At this point, we have:

So, ∠CEB = 90° + 24° = 114°

Answer: A

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In the figure AB and CD are two diameters of circle. Interse 03 Aug 2014, 02:46
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In the figure AB and CD are two diameters of circle. Intersecting at angle 48 degree. E is any point on Arc CB. find angle CEB

A 114
B 100
C 80
D 96
E 40
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Kudos from me, because I love problems with central angles:)
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In the figure AB and CD are two diameters of circle. Interse 03 Aug 2014, 03:47
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smyarga
Since, CD and AB are two diameters of the circle, so their intersection is the centre. Let's denote this centre O. Angle CEB is inscribed, and angle COB is corresponding central angle (arc CAB). The value of angle COB=180+48=228 degrees. The measure of inscribed angle is always half the measure of the central angle. Angle CEB is equal =228/2=114 degrees.

The correct answer is A.
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Hi,

I thought angle COB is 180-42=138 degrees. You have derived angle COB of 228 degrees.
Can you please explain.
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In the figure AB and CD are two diameters of circle. Interse 03 Aug 2014, 19:52
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desaichinmay22
smyarga
Since, CD and AB are two diameters of the circle, so their intersection is the centre. Let's denote this centre O. Angle CEB is inscribed, and angle COB is corresponding central angle (arc CAB). The value of angle COB=180+48=228 degrees. The measure of inscribed angle is always half the measure of the central angle. Angle CEB is equal =228/2=114 degrees.

The correct answer is A.


Hi,

I thought angle COB is 180-42=138 degrees. You have derived angle COB of 228 degrees.
Can you please explain.
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According to me, CB is not the diameter. So central angle doesnt apply in this case. Also, COB is 138 and not 228.
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In the figure AB and CD are two diameters of circle. Interse 04 Aug 2014, 06:02
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desaichinmay22
smyarga
Since, CD and AB are two diameters of the circle, so their intersection is the centre. Let's denote this centre O. Angle CEB is inscribed, and angle COB is corresponding central angle (arc CAB). The value of angle COB=180+48=228 degrees. The measure of inscribed angle is always half the measure of the central angle. Angle CEB is equal =228/2=114 degrees.

The correct answer is A.


Hi,

I thought angle COB is 180-42=138 degrees. You have derived angle COB of 228 degrees.
Can you please explain.
Show more

Hi buddy,

COB is indeed 180-48 = 132 degrees . There is a concept of major and minor segment ( please google this ) Now the point O is in the minor segment of the arc and in this case it would be half of the angle subtended in the major segment i.e ( 360-132) = 228 /2 = 114 .
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In the figure AB and CD are two diameters of circle. Interse 04 Aug 2014, 06:58
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Since, CD and AB are two diameters of the circle, so their intersection is the centre. Let's denote this centre O. Angle CEB is inscribed, and angle COB is corresponding central angle (arc CAB). The value of angle COB=180+48=228 degrees. The measure of inscribed angle is always half the measure of the central angle. Angle CEB is equal =228/2=114 degrees.

The correct answer is A.


Hi,

I thought angle COB is 180-42=138 degrees. You have derived angle COB of 228 degrees.
Can you please explain.

That's why I mentioned arc CAB. You don't really need to understand the notions of major and minor arc. Corresponding central angle means that it stays on the same arc as your inscribed angle.
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Now I got the explanation. Thanks for the help.
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In the figure AB and CD are two diameters of circle. Interse 04 Aug 2014, 13:31
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desaichinmay22, specially for you another nice problem with central angle if-the-radius-of-the-circle-below-see-attachment-is-equal-175709.html
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In the figure AB and CD are two diameters of circle. Interse 05 Aug 2014, 06:51
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smyarga
Since, CD and AB are two diameters of the circle, so their intersection is the centre. Let's denote this centre O. Angle CEB is inscribed, and angle COB is corresponding central angle (arc CAB). The value of angle COB=180+48=228 degrees. The measure of inscribed angle is always half the measure of the central angle. Angle CEB is equal =228/2=114 degrees.

The correct answer is A.


Hi,

I thought angle COB is 180-42=138 degrees. You have derived angle COB of 228 degrees.
Can you please explain.

That's why I mentioned arc CAB. You don't really need to understand the notions of major and minor arc. Corresponding central angle means that it stays on the same arc as your inscribed angle.
Show more

Hi Smyarga,
how did you get 180 degrees?
i thought about vertically opposite angles then realised that i was wrong.
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In the figure AB and CD are two diameters of circle. Interse 05 Aug 2014, 07:07
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desaichinmay22



Hi,

I thought angle COB is 180-42=138 degrees. You have derived angle COB of 228 degrees.
Can you please explain.

That's why I mentioned arc CAB. You don't really need to understand the notions of major and minor arc. Corresponding central angle means that it stays on the same arc as your inscribed angle.


Hi Smyarga,
how did you get 180 degrees?
i thought about vertically opposite angles then realised that i was wrong.
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Since COD is straight.
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In the figure AB and CD are two diameters of circle. Interse 06 Aug 2014, 04:25
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In the figure AB and CD are two diameters of circle. Intersecting at angle 48 degree. E is any point on Arc CB. find angle CEB

A 114
B 100
C 80
D 96
E 40
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Join Segment AE in the figure, we know Angle AEC is half of Angle COA(Assuming diameter intersect at point O).

Angle AEC = 24
Ab is diameter, so Angle AEB = 90
Angle CEB = 90+24 = 114
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In the figure AB and CD are two diameters of circle. Interse 28 Aug 2014, 20:07
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Hi there,
Can someone explain me this with the help of proper diagram,unable to get it!
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In the figure AB and CD are two diameters of circle. Interse 04 Dec 2014, 00:07
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Since, CD and AB are two diameters of the circle, so their intersection is the centre. Let's denote this centre O. Angle CEB is inscribed, and angle COB is corresponding central angle (arc CAB). The value of angle COB=180+48=228 degrees. The measure of inscribed angle is always half the measure of the central angle. Angle CEB is equal =228/2=114 degrees.

The correct answer is A.


Hi,

I thought angle COB is 180-42=138 degrees. You have derived angle COB of 228 degrees.
Can you please explain.

That's why I mentioned arc CAB. You don't really need to understand the notions of major and minor arc. Corresponding central angle means that it stays on the same arc as your inscribed angle.
Show more


another approach,

join C and A. since AB is the diameter, A, C, E and B form a cyclic quadrilateral. now opposit angles of cyclic quadrilaterals sum up to 180 degrees. considering the point of intersection of the 2 diameters as O.

angle AOC = 48 degrees. ........... given
OA = OC, radius of the circle, hence trianlge OAC is isoceles.
thus angle ACO = angle OAC = 66 degrees.

now,
angle OAC + angle CEB = 180 degrees......... since opposit angles of cyclic quadrilaterals sum up to 180 degrees.
therefore, angle CEB = 180 - 66 = 114 degrees.

hope this was helpful.

kudos if you like. :)
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In the figure AB and CD are two diameters of circle. Interse Updated on: 27 Nov 2021, 09:01
Originally posted by BrushMyQuant on 14 Dec 2014, 21:42.
Last edited by BrushMyQuant on 27 Nov 2021, 09:01, edited 1 time in total.
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Please tag this to PS instead of DS
Thank you!

Watch the following video to Learn Basics of Circles

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In the figure AB and CD are two diameters of circle. Interse 15 Dec 2014, 08:11
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Please tag this to PS instead of DS
Thank you!
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Moved to PS forum. Thank you for noticing this.
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In the figure AB and CD are two diameters of circle. Interse 18 Dec 2014, 04:32
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Hi,

Can any1 explain me how angle COB=180 degrees. Why is the sum 180+48?
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In the figure AB and CD are two diameters of circle. Interse 18 Dec 2014, 05:04
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Hi,

Can any1 explain me how angle COB=180 degrees. Why is the sum 180+48?
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Angle COB is not 180.

Note that the angle around O will be 360 degrees. There is angle COB, the smaller angle (the angle that arc CEB subtends at the center) and angle COB, the larger angle (shown by red arrow around center O in the second diagram). The major arc CADB subtends larger angle COB at the center and inscribed angle CEB at the circle. The central angle will be twice the inscribed angle.

The larger angle COB = angle COA + angle AOD + angle DOB = 180 + 48 = 228 = Central angle

Inscribed angle = 228/2 = 114

Answer (A)
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In the figure AB and CD are two diameters of circle. Interse 24 Oct 2015, 06:31
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Hi,

Can any1 explain me how angle COB=180 degrees. Why is the sum 180+48?

Angle COB is not 180.

Note that the angle around O will be 360 degrees. There is angle COB, the smaller angle (the angle that arc CEB subtends at the center) and angle COB, the larger angle (shown by red arrow around center O in the second diagram). The major arc CADB subtends larger angle COB at the center and inscribed angle CEB at the circle. The central angle will be twice the inscribed angle.

The larger angle COB = angle COA + angle AOD + angle DOB = 180 + 48 = 228 = Central angle

Inscribed angle = 228/2 = 114

Answer (A)
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Hi Karishma

can't we take this way that smaller COB is 132 and then CEB = 180 - (132/2) ? using cyclic quadrilateral property.
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