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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

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

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

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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

Source: Veritas Prep

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Source: Beat The GMAT — Data Sufficiency | Sun Feb 24, 2019 6:59 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

edited

by deloitte247 » Thu Mar 07, 2019 7:33 am

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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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