MathDB

GH // t wanted, 4 concyclic points, tangent, reflection of AB wrt AC

Source: Switzerland - Swiss MO 2014 p1

July 16, 2020

geometryreflectioncyclic quadrilateralparallel

Problem Statement

The points

A, B, C

and

D

lie in this order on the circle

k

. Let

t

be the tangent at

k

through

C

and

s

the reflection of

AB

AC

. Let

G

be the intersection of the straight line

AC

and

BD

and

H

the intersection of the straight lines

s

and

CD

. Show that

GH

is parallel to

t