MathDB

2012 ToT Spring Senior O p4 locus is a circle, cyclic ABCD given

Source:

March 5, 2020

geometryCyclicLocuscirclestangent circles

Problem Statement

A quadrilateral

ABCD

with no parallel sides is inscribed in a circle. Two circles, one passing through

A

and

B

, and the other through

C

and

D

, are tangent to each other at

X

. Prove that the locus of

X

is a circle.