MathDB

Centre of square is collinear with intersections of k and k'

Source: Baltic Way 2010

November 19, 2010

geometry proposedgeometry

Problem Statement

Let

ABCD

be a square and let

S

be the point of intersection of its diagonals

AC

and

BD

. Two circles

k,k'

go through

A,C

and

B,D

; respectively. Furthermore,

k

and

k'

intersect in exactly two different points

P

and

Q

. Prove that

S

lies on

PQ