MathDB

In a scalene triangle

ABC

H

is the orthocenter, and

G

is the centroid. Let

A_b

and

A_c

be points on

AB

and

AC

, respectively, such that

B

C

A_b

A_c

are cyclic, and the points

A_b

A_c

H

are collinear.

O_a

is the circumcenter of the triangle

AA_bA_c

O_b

and

O_c

are defined similarly. Prove that the centroid of the triangle

O_aO_bO_c

lies on the line

HG

Problem Statement