MathDB

3 lines concurrency , 4 circles related, cyclic ABCD related

Source: Tournament of Towns, Senior A-Level Paper, Spring 2020 , p5

June 3, 2020

geometryconcurrencyconcurrentcyclic quadrilateralcircles

Problem Statement

Let

ABCD

be an inscribed quadrilateral. Let the circles with diameters

AB

and

CD

intersect at two points

X_1

and

Y_1

, the circles with diameters

BC

and

AD

intersect at two points

X_2

and

Y_2

, the circles with diameters

AC

and

BD

intersect at two points

X_3

and

Y_3

. Prove that the lines

X_1Y_1, X_2Y_2

and

X_3Y_3

are concurrent.
Maxim Didin