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605-655 (Medium)|   Geometry|      
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pushkarajnjadhav
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In the given figure, O is the center of the circle 22 Aug 2017, 10:19
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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45% (medium)

Question Stats:

66% (02:22) correct 34% (02:16) wrong based on 121 sessions

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In the given figure, O is the center of the circle; ∠ OAB= 80° and ∠ OCB= 70°, What is the measure of ∠ AOC ?

A) 120°
B) 60°
C) 150°
D) 100°
E) 80°

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B
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pushkarajnjadhav
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In the given figure, O is the center of the circle Updated on: 09 Sep 2023, 11:16
Originally posted by pushkarajnjadhav on 22 Aug 2017, 11:24.
Last edited by Bunuel on 09 Sep 2023, 11:16, edited 2 times in total.
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Hi akshata19,
here is an alternate approach.
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In the given figure, O is the center of the circle 22 Aug 2017, 10:46
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pushkarajnjadhav
In the given figure, O is the center of the circle; ∠ OAB= 80° and ∠ OCB= 70°, What is the measure of ∠ AOC ?

A) 120°
B) 60°
C) 150°
D) 100°
E) 80°

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Hi..
OAB is 80 and OCB is 70..
So remaining two angles sum : AOC+ABC=360-(80+70)=210..(i)
Also if AOC is extended to the circumference AO'C=AOC/2
And AO'C+ABC=180......AOC/2 + ABC=180....(ii)

From i and ii
AOC/2=30...AOC=30*2=60

B
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In the given figure, O is the center of the circle 22 Aug 2017, 11:05
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∠ OAB + ∠ OCB + ∠ AOC + ∠ ABC =360

80+70+ ∠ AOC + ∠ ABC =360

∠ AOC + ∠ ABC = 210
∠ AOC + 1/2 ∠X = 210 (property of inscribed angle... Here X is the angle measure of larger ARC AOC)

∠ AOC + 1/2 (360 - ∠ AOC) = 210 (property - measure at a point is 360)


Solving we get,
∠ AOC=60

Any other easy way to solve this..?

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In the given figure, O is the center of the circle 22 Aug 2017, 11:31
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Clearly answer is B
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TheNightKing
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In the given figure, O is the center of the circle 21 Sep 2019, 08:37
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pushkarajnjadhav
In the given figure, O is the center of the circle; ∠ OAB= 80° and ∠ OCB= 70°, What is the measure of ∠ AOC ?

A) 120°
B) 60°
C) 150°
D) 100°
E) 80°

Kudos if it helps.
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Notice that AOC + 2(ABC) should give you 360 because it is a circle.

AOC+ABC=210 ....sum of angles of a quadrilateral should be 360.
If AOC is 60 then ABC is 150. Double of ABC will be 300. The sum will be 360 which forms the circle. Hence B.

Thank you!
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In the given figure, O is the center of the circle 09 Sep 2023, 11:04
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