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Bosnia and Herzegovina 2018 TST Day 1 Problem 1

Source: Bosnia and Herzegovina 2018 TST

September 15, 2018

geometryperpendicularorthocenter

Problem Statement

In acute triangle

ABC

(AB < AC)

let

AB

,

E

and

F

be foots of perpedicular from

A

,

B

and

C

to

BC

,

CA

and

AB

, respectively. Let

P

and

Q

be points on line

EF

such that

DP \perp EF

and

BQ=CQ

. Prove that

\angle ADP = \angle PBQ

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