MathDB

ASU 177 All Soviet Union MO 1973 equal segments, circle tangent to angle

Source:

July 4, 2019

geometryequal segments

Problem Statement

Given an angle with the vertex

O

and a circle touching its sides in the points

A

and

B

. A ray is drawn from the point

A

parallel to

[OB)

. It intersects with the circumference in the point

C

. The segment

[OC]

intersects the circumference in the point

E

. The straight lines

(AE)

and

(OB)

intersect in the point

K

. Prove that

|OK| = |KB|