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equal segments wanted, tangents form endpoints of a diameter related

Source: Austrian-Polish 1980

May 25, 2019

geometryequal segmentsTangentscircle

Problem Statement

Through the endpoints

A

and

B

of a diameter

AB

of a given circle, the tangents

\ell

and

m

have been drawn. Let

C\ne A

be a point on

D_i

and let

q_1,q_2

be two rays from

C

. Ray

q_i

cuts the circle in

D_i

and

E_i

with

D_i

between

C

and

E_i, i = 1,2

. Rays

AD_1,AD_2,AE_1,AE_2

meet

m

in the respective points

M_1,M_2,N_1,N_2

. Prove that

M_1M_2 = N_1N_2

.

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