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Geometry with right angles and length conditions

Source: Baltic Way 2018, Problem 12

November 6, 2018

geometry

Problem Statement

The altitudes

BB_1

and

CC_1

of an acute triangle

ABC

intersect in point

H

. Let

B_2

and

C_2

be points on the segments

BH

and

CH

, respectively, such that

BB_2=B_1H

and

CC_2=C_1H

. The circumcircle of the triangle

B_2HC_2

intersects the circumcircle of the triangle

ABC

in points

D

and

E

. Prove that the triangle

DEH

is right-angled.

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