MathDB

China 2010 quiz1 Problem 2

Source:

September 5, 2010

geometrycircumcircletrigonometryparallelogramgeometry unsolved

Problem Statement

Let

ABCD

be a convex quadrilateral. Assume line

AB

and

CD

intersect at

E

, and

B

lies between

A

and

E

. Assume line

AD

and

BC

intersect at

F

, and

D

lies between

A

and

F

. Assume the circumcircles of

\triangle BEC

and

\triangle CFD

intersect at

C

and

P

. Prove that

\angle BAP=\angle CAD

if and only if

BD\parallel EF

.

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