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BD+BE=2CH

Source: Saint Petersburg olympiad 2024, 9.5

September 22, 2024

geometry

Problem Statement

Let

AH

be altitude in acute trinagle

ABC

, inscribed in circle

s

. Points

D

and

E

are chosen on segment

BH

. Points

X

and

Y

are chosen on rays

AD

and

AE

, respectively, such that midpoints of segments

DX

and

EY

lies on

s

. Suppose that points

B

,

X

,

Y

and

C

are concyclic. Prove that

BD+BE=2CH

.

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