MathDB

Three points collinear

Source: Bosnia and Herzegovina Team Selection Test 2005 problem 1 day 2

October 6, 2017

geometrydiametertangentcollinear

Problem Statement

On the line which contains diameter

PQ

of circle

k(S,r)

, point

A

is chosen outside the circle such that tangent

t

from point

A

touches the circle in point

T

. Tangents on circle

k

in points

P

and

Q

are

p

and

q

, respectively. If

PT \cap q={N}

and

QT \cap p={M}

, prove that points

A

M

and

N

are collinear.