MathDB

Geometry problem

Source: Polish National Olympiad 2015 2nd round, 6th problem

March 3, 2015

geometrycircumcircle

Problem Statement

Let

ABC

be a triangle. Let

K

be a midpoint of

BC

and

M

be a point on the segment

AB

.

L=KM \cap AC

and

C

lies on the segment

AC

between

A

and

L

. Let

N

be a midpoint of

ML

.

AN

cuts circumcircle of

\Delta ABC

in

S

and

S \neq N

. Prove that circumcircle of

\Delta KSN

is tangent to

BC

.

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