MathDB

Cyclic Points

Source: EGMO 2017 Day1 P1

April 8, 2017

cylicgeometryAngle ChasingquadrilateralEGMOEGMO 2017barycentric coordinates

Problem Statement

Let

ABCD

be a convex quadrilateral with

\angle DAB=\angle BCD=90^{\circ}

and

\angle ABC> \angle CDA

. Let

Q

and

R

be points on segments

BC

and

CD

, respectively, such that line

QR

intersects lines

AB

and

AD

at points

P

and

S

, respectively. It is given that

PQ=RS

.Let the midpoint of

BD

be

M

and the midpoint of

QR

be

N

.Prove that the points

M,N,A

and

C

lie on a circle.

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