MathDB

A,P,Q are collinear iff AC=AB\sqrt2 (2013 Romania District VII P3)

Source:

May 20, 2020

geometrycollinearequal anglesmidpoint

Problem Statement

On the sides

(AB)

and

(AC)

of the triangle

ABC

are considered the points

M

and

N

respectively so that

\angle ABC =\angle ANM

. Point

D

is symmetric of point

A

with respect to

B

, and

P

and

Q

are the midpoints of the segments

[MN]

and

[CD]

, respectively. Prove that the points

A, P

and

Q

are collinear if and only if

AC = AB \sqrt {2}

Back to Problems View on AoPS