MathDB

Let

{c\equiv c\left(O, R\right)}

be a circle with center

{O}

and radius

{R}

and

{A, B}

be two points on it, not belonging to the same diameter. The bisector of angle

{\angle{ABO}}

intersects the circle

{c}

at point

{C}

, the circumcircle of the triangle

AOB

, say

{c_1}

at point

{K}

and the circumcircle of the triangle

AOC

, say

{{c}_{2}}

at point

{L}

. Prove that point

{K}

is the circumcircle of the triangle

AOC

and that point

{L}

is the incenter of the triangle

AOB

.
Evangelos Psychas (Greece)

Problem Statement