MathDB

The circle with the center of

O

touches the sides of the angle

A

at the points of

K

and

M

. The tangent to the circle intersects the segments

AK

and

AM

at points

B

and

C

respectively, and the line

KM

intersects the segments

OB

and

OC

at the points

D

and

E

. Prove that the area of the triangle

ODE

is equal to a quarter of the area of a triangle

BOC

if and only if the angle

A

60^\circ

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