MathDB

EF bisects A'K in triangle with 45° angle

Source: Sharygin 2019 Finals Day 1 Grade 10 P1

July 30, 2019

geometry

Problem Statement

Given a triangle

ABC

with

\angle A = 45^\circ

. Let

A'

be the antipode of

A

in the circumcircle of

ABC

. Points

E

and

F

on segments

AB

and

AC

respectively are such that

A'B = BE

,

A'C = CF

. Let

K

be the second intersection of circumcircles of triangles

AEF

and

ABC

. Prove that

EF

bisects

A'K

.

Back to Problems View on AoPS