MathDB

Let

ABCD

be an inscribed quadrilateral in a circle

c(O,R)

(of circle

O

and radius

R

). With centers the vertices

A,B,C,D

, we consider the circles

C_{A},C_{B},C_{C},C_{D}

respectively, that do not intersect to each other . Circle

C_{A}

intersects the sides of the quadrilateral at points

A_{1} , A_{2}

, circle

C_{B}

intersects the sides of the quadrilateral at points

B_{1} , B_{2}

, circle

C_{C}

at points

C_{1} , C_{2}

and circle

C_{D}

at points

C_{1} , C_{2}

. Prove that the quadrilateral defined by lines

A_{1}A_{2} , B_{1}B_{2} , C_{1}C_{2} , D_{1}D_{2}

is cyclic.

2