MathDB

Excircle tangent to symmedian

Source: Own/Folklore

July 4, 2024

geometryconfig geosymmedianexcircle

Problem Statement

Let

ABC

be a triangle and let

X

and

Y

be points on the

A

-symmedian such that

AX = XB

and

AY = YC

. Let

BX

and

CY

meet at

Z

. Let the

Z

-excircle of triangle

XYZ

touch

ZX

and

ZY

at

E

and

F

. Show that

A

,

E

,

F

are collinear.

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