MathDB

5AB = 4BC, <B = 60

Source: Philippines MO 2018/1

August 4, 2018

geometry

Problem Statement

In triangle

ABC

with

\angle ABC = 60^{\circ}

and

5AB = 4BC

, points

D

and

E

are the feet of the altitudes from

B

and

C

, respectively.

M

is the midpoint of

BD

and the circumcircle of triangle

BMC

meets line

AC

again at

N

. Lines

BN

and

CM

meet at

P

. Prove that

\angle EDP = 90^{\circ}

.

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