MathDB

In the acute-angle triangle

ABC

we have

\angle ACB = 45^\circ

. The points

A_1

and

B_1

are the feet of the altitudes from

A

and

B

, and

H

is the orthocenter of the triangle. We consider the points

D

and

E

on the segments

AA_1

and

BC

such that

A_1D = A_1E = A_1B_1

. Prove that a)

A_1B_1 = \sqrt{ \frac{A_1B^2+A_1C^2}{2} }

; b)

CH=DE

Problem Statement