MathDB

Two circles intersecting on circumcircle

Source: 2023 Turkey TST D2 P5

March 29, 2023

geometrycircumcircleincenter

Problem Statement

Let

ABC

be a scalene triangle with circumcentre

O

, incentre

I

and orthocentre

H

. Let the second intersection point of circle which passes through

O

and tangent to

IH

at point

I

, and the circle which passes through

H

and tangent to

IO

at point

I

M

. Prove that

M

lies on circumcircle of

ABC