MathDB

Tangents

l_1

and

l_2

common to circles

c_1

and

c_2

intersect at point

P

, whereby tangent points remain to different sides from

P

on both tangent lines. Through some point

T

, tangents

p_1

and

p_2

to circle

c_1

and tangents

p_3

and

p_4

to circle

c_2

are drawn. The intersection points of

l_1

with lines

p_1, p_2, p_3, p_4

are

A_1, B_1, C_1, D_1

, respectively, whereby the order of points on

l_1

is:

A_1, B_1, P, C_1, D_1

. Analogously, the intersection points of

l_2

with lines

p_1, p_2, p_3, p_4

are

A_2, B_2, C_2, D_2

, respectively. Prove that if both quadrangles

A_1A_2D_1D_2

and

B_1B_2C_1C_2

are cyclic then radii of

c_1

and

c_2

are equal.

Problem Statement