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In the figure shown, point O is the center of the circle and

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by BTGmoderatorDC » Sun Feb 24, 2019 6:59 am

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00:00

Answers

A

B

C

D

E

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In the figure shown, point O is the center of the circle and points B, C, and D lie on the circle. If the segment AB is equal to the length of line segment OC, what is the degree measure of angle BAO?

(1) The degree measure of angle COD is 60
(2) The degree measure of angle BCO is 40

OA D

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Source: — Data Sufficiency |
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edited

by deloitte247 » Thu Mar 07, 2019 7:33 am
BO = CO = radius = AB
Triangles BOC and ABO are Isosceles (i.e 2 sides have equal length)
Therefore,
<BAO = <BOA and <BCO = < CBO
<CBO = 2*<BOA and <BAO = CBO/2

Statement 1
The degree measure of <COD = 60 degree
<BAO + ACO = <COD where COD = 60 deg
Using exterior angle theorem
<ACO = <CBO = 2*<BAO
So, <BAO + ACO = 2*BAO + BAO = 3<BAO = 60 deg
BAO = 60/3 = 20 degree
Hence, statement 1 is INSUFFICIENT.

Statement 2
The degree measure of angle BCO is 40 deg
<BCO = 40
<BCO = CBO = 40deg
2<BAO = 40deg
2BAO = 40/2 =20deg
Statement 2 is INSUFFICIENT.

$$answer\ is\ Option\ D$$
Last edited by deloitte247 on Thu Mar 07, 2019 7:42 am, edited 1 time in total.
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by Ian Stewart » Thu Mar 07, 2019 7:40 am
This is exactly identical to a GMATPrep question:

https://gmatclub.com/forum/in-the-figur ... 89662.html
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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