MathDB

Geometry problem

Source: Moldova TST 2018

April 6, 2018

geometry

Problem Statement

Let

\Omega

be the circumcincle of the quadrilateral

ABCD

, and

E

the intersection point of the diagonals

AC

and

BD

. A line passing through

E

intersects

AB

and

BC

in points

B,P,Q,

and

Q

. A circle ,that is passing through point

D

, is tangent to the line

PQ

in point

E

and intersects

\Omega

in point

R

, different from

D

. Prove that the points

B,P,Q,

and

R

are concyclic .

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