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

[BTGmoderatorDC]

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

[deloitte247]

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.

$$answer\ is\ Option\ D$$

[Ian Stewart]

This is exactly identical to a GMATPrep question:

https://gmatclub.com/forum/in-the-figur ... 89662.html