Geometry

[shovan85]

I have the OA will send later. This is an actual q from GMAT prep sw. Got it wrong and not able to prove the OA. Plz Help!!!
from B we can get answer but how to get the same from A?

[clock60]

this is very unpleasant problem
at first some notes, we see, as ab=oc=bo ( oc=ob=radiu of the circle). it means that triangle abo isosceles. and angle bao=boa=x, we also need another angle cod=y, and one point on the line ad between a and o, say e
and now very important property to solve this task in a least amount of time
angle x=( arc cd-arc be)/2.
arc cd=angle y, ( as o is the center of the circle)
arc be=angle x, so needed value
x=(y-x)/2, 2x=y-x. 3x=y. if we find one of the angles x or y the problem will be solved, to the st
(1) y=60, 3x=60,x=20 suff

(2)triangle bco isosceles. with two angles =40 and the third angle=100
x+y+100=180
x+y=80
x+3x=80, 4x=80 x=20 also suff
my answer is D

[shovan85]

HI clock60,

Thanks. OA is D.

Can you please send me any related link or source name where you got this property:
angle x=( arc cd-arc be)/2.

Thanks,
Shovan