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midpoint wanted, staring with an isosceles ABC and circle (A, AB=AC)

Source: Switzerland - Swiss ΜΟ 2017 p8

July 14, 2020

geometrymidpointisoscelesequal segments

Problem Statement

Let

ABC

be an isosceles triangle with vertex

k

and

ABC

. Let

k

be the circle with center

A

passsing through

B

and

C

. Let

H

be the second intersection of

k

with the altitude of the triangle

ABC

through

B

. Further let

G

be the second intersection of

k

with the median through

B

in triangle

ABC

. Let

X

be the intersection of the lines

AC

and

GH

. Show that

C

is the midpoint of

AX

.

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