MathDB

Let

ABC

be an acute triangle with side

AB

of length

1

. Say we reflect the points

A

and

B

across the midpoints of

BC

and

AC

, respectively to obtain the points

A’

and

B’

. Assume that the orthocenters of triangles

ABC

A’BC

and

B’AC

form an equilateral triangle. a) Prove that triangle

ABC

is isosceles. b) What is the length of the altitude of

ABC

through

C

Problem Statement