MathDB

collinear wanted, circle intersecting a square (2017 Kyiv City MO 8.4)

Source:

September 8, 2020

geometrysquarecollinear

Problem Statement

On the sides

BC

and

CD

of the square

ABCD

, the points

M

and

N

are selected in such a way that

\angle MAN= 45^o

. Using the segment

MN

, as the diameter, we constructed a circle

w

, which intersects the segments

AM

and

AN

at points

P

and

Q

, respectively. Prove that the points

B, P

and

Q

lie on the same line.