MathDB

cyclics quadrilaterals

Source: Mathematics Regional Olympiad of Mexico Southeast 2016 P2

October 25, 2021

geometrytrapezoidcircumcirclecyclic quadrilateral

Problem Statement

Let

ABCD

a trapezium with

AB

parallel to

CD, \Omega

the circumcircle of

ABCD

and

A_1,B_1

points on segments

AC

and

BC

respectively, such that

DA_1B_1C

is a cyclic cuadrilateral. Let

A_2

and

B_2

the symmetric points of

A_1

and

B_1

with respect of the midpoint of

AC

and

BC

, respectively. Prove that points

A, B, A_2, B_2

are concyclic.