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In the circle above the length of the minor arc AB is 10pi and the [#permalink]

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24 Aug 2016, 02:45

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Question Stats:

57% (02:41) correct 43% (02:30) wrong based on 72 sessions

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In the circle above the length of the minor arc AB is 10pi and the length of the minor arc CD is 3pi. What is the measure of angle F, if the radius of the circle is 18?

Re: In the circle above the length of the minor arc AB is 10pi and the [#permalink]

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24 Aug 2016, 03:57

Stn wrote:

In the circle above the length of the minor arc AB is 10pi and the length of the minor arc CD is 3pi. What is the measure of angle E, if the radius of the circle is 18?

Source: OptimusPrep

Is it 70 degree?

Angle of Major Arc - Angle of Minor Arc = 100 - 30 = 70 Degree. (Not Sure about this).

Cheers Balaji
_________________

Aiming for a 3 digit number with 7 as hundredths Digit

In the circle above the length of the minor arc AB is 10pi and the [#permalink]

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24 Aug 2016, 07:43

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The only thing you need to remember while solving this question is the arc rule.

Arc rule: The angle subtended by the arc at the center is always twice the angle subtended by it at any other point on the circle.

IN this question since arc AB=10pi and arc CD=3pi and circumference=2.pi.r =2.pi.18 =36pi, we can calculate the angle subtended by the arcs at the center as,

3pi/36pi = 1/12 =1/12th of whole angle =360 * 1/12 = 30 and thus making angle CBD as 15degrees. (Coz the arc CD subtends 30deg at center, it will subtend 15deg at any other point on circumference of circle, in this case pt B)

Next, 10pi/36pi = 10/36th of whole angle = 360 * 10/36 = 100 and thus making angle ACB as 50 degrees. Now In TRIANGLE CBF, angle B(CBD) =15 angle C(BCF) =130 thus angle F= 180 - (B + C) = 180 - 145 = 35

Re: In the circle above the length of the minor arc AB is 10pi and the [#permalink]

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24 Aug 2016, 08:04

My Approach:

CB is diameter, A is a point on the semi circle..so Angle A will be 90 degrees. Given radius = 18. So the length of the arc BAC is 18pi. Given AB = 10pi So AC = 8pi

AC = 8pi, CD = 3pi, So AD = 11pi. At centre, AD subtends and angle 110 degrees.( By comparing 18pi spans 180 degrees) So at B, AD subtends an angle of 110/2 = 55 degrees

90 degrees + 55 degrees + Angle at F = 180 degrees. Therefore F = 35 degrees

Re: In the circle above the length of the minor arc AB is 10pi and the [#permalink]

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28 Apr 2017, 02:59

Stn wrote:

In the circle above the length of the minor arc AB is 10pi and the length of the minor arc CD is 3pi. What is the measure of angle F, if the radius of the circle is 18?

(A) 20 (B) 25 (C) 30 (D) 35 (E) 40

Source: OptimusPrep

LE: Updated. Had some editing issues first time.

CB or CB is diameter how can you assume that its not given in the question stem?? and by any means with the help of info given in the question can you prove CB is the diameter??

Re: In the circle above the length of the minor arc AB is 10pi and the [#permalink]

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28 Apr 2017, 07:29

shashanksst94 wrote:

The only thing you need to remember while solving this question is the arc rule.

Arc rule: The angle subtended by the arc at the center is always twice the angle subtended by it at any other point on the circle.

IN this question since arc AB=10pi and arc CD=3pi and circumference=2.pi.r =2.pi.18 =36pi, we can calculate the angle subtended by the arcs at the center as,

3pi/36pi = 1/12 =1/12th of whole angle =360 * 1/12 = 30 and thus making angle CBD as 15degrees. (Coz the arc CD subtends 30deg at center, it will subtend 15deg at any other point on circumference of circle, in this case pt B)

Next, 10pi/36pi = 10/36th of whole angle = 360 * 10/36 = 100 and thus making angle ACB as 50 degrees. Now In TRIANGLE CBF, angle B(CBD) =15 angle C(BCF) =130 thus angle F= 180 - (B + C) = 180 - 145 = 35

(D)

Can someone please explain how we arrived at angle C (BCF) = 130?

Re: In the circle above the length of the minor arc AB is 10pi and the [#permalink]

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02 Oct 2017, 02:06

shashanksst94 wrote:

The only thing you need to remember while solving this question is the arc rule.

Arc rule: The angle subtended by the arc at the center is always twice the angle subtended by it at any other point on the circle.

IN this question since arc AB=10pi and arc CD=3pi and circumference=2.pi.r =2.pi.18 =36pi, we can calculate the angle subtended by the arcs at the center as,

3pi/36pi = 1/12 =1/12th of whole angle =360 * 1/12 = 30 and thus making angle CBD as 15degrees. (Coz the arc CD subtends 30deg at center, it will subtend 15deg at any other point on circumference of circle, in this case pt B)

Next, 10pi/36pi = 10/36th of whole angle = 360 * 10/36 = 100 and thus making angle ACB as 50 degrees. Now In TRIANGLE CBF, angle B(CBD) =15 angle C(BCF) =130 thus angle F= 180 - (B + C) = 180 - 145 = 35

(D)

Hi , But what if BC is not the diameter of the circle? It is not given in the question. Can we solve the question the same way without this info?