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Problem 4 -- Pentagon Proof

Source: 47th Austrian Mathematical Olympiad Beginners' Competition Problem 4

July 27, 2018

Austriageometrypentagon

Problem Statement

Let

ABCDE

be a convex pentagon with ﬁve equal sides and right angles at

C

and

D

. Let

P

denote the intersection point of the diagonals

AC

and

BD

. Prove that the segments

PA

and

PD

have the same length.
(Gottfried Perz)