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Angles in cyclic quadrilateral - Iran First Round 2018, P20

Source:

March 7, 2021

geometrycyclic quadrilateral

Problem Statement

In the convex and cyclic quadrilateral

ABCD

, we have

\angle B = 110^{\circ}

. The intersection of

AD

and

BC

is

E

and the intersection of

AB

and

CD

is

F

. If the perpendicular from

E

to

AB

intersects the perpendicular from

F

to

BC

on the circumcircle of the quadrilateral at point

P

, what is

\angle PDF

in degrees?

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