MathDB

Concyclic points

Source: Baltic Way 2014, Problem 14

November 11, 2014

geometrycircumcirclegeometry proposed

Problem Statement

Let

ABCD

be a convex quadrilateral such that the line

BD

bisects the angle

ABC.

The circumcircle of triangle

ABC

intersects the sides

AD

and

CD

in the points

P

and

Q,

respectively. The line through

D

and parallel to

AC

intersects the lines

BC

and

BA

at the points

R

and

S,

respectively. Prove that the points

P, Q, R

and

S

lie on a common circle.

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