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Tangent lines

Source: St Petersburg Olympiad 2018, Grade 11, P7

June 21, 2018

geometry

Problem Statement

Points

A,B

lies on the circle

S

. Tangent lines to

S

at

A

and

B

intersects at

C

.

M

-midpoint of

AB

. Circle

S_1

goes through

M,C

and intersects

AB

at

D

and

S

at

K

and

L

. Prove, that tangent lines to

S

at

K

and

L

intersects at point on the segment

CD

.

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