MathDB

Reflection of arc midpoint w.r.t side of triangle lies on some line

Source: Tuymaada 2019 P8

July 15, 2019

geometrygeometric transformationreflectionarc midpointcircumcirclemoving pointsInversion

Problem Statement

\triangle ABC

\angle B

is obtuse and

AB \ne BC

. Let

O

is the circumcenter and

\omega

is the circumcircle of this triangle.

N

is the midpoint of arc

ABC

. The circumcircle of

\triangle BON

intersects

AC

on points

X

and

Y

. Let

BX \cap \omega = P \ne B

and

BY \cap \omega = Q \ne B

. Prove that

P, Q

and reflection of

N

with respect to line

AC

are collinear.