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p6 geometry

Source: Turkey TST 2020 Day 2 P6

March 10, 2020

geometry

Problem Statement

In a triangle

\triangle ABC

,

D

and

E

are respectively on

M

and

AC

such that

DE\parallel BC

.

P

is the intersection of

BE

and

CD

.

M

is the second intersection of

(APD)

and

(BCD)

,

N

is the second intersection of

(APE)

and

(BCE)

.

w

is the circle passing through

M

and

N

and tangent to

BC

. Prove that the lines tangent to

w

at

M

and

N

intersect on

AP

.

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