MathDB

Let

ABCD

be a quadrilateral inscribed in a unit circle with center

O

. Suppose that

\angle AOB = \angle COD = 135^\circ

BC=1

. Let

B^\prime

and

C^\prime

be the reflections of

A

across

BO

and

CO

respectively. Let

H_1

and

H_2

be the orthocenters of

AB^\prime C^\prime

and

BCD

, respectively. If

M

is the midpoint of

OH_1

, and

O^\prime

is the reflection of

O

about the midpoint of

MH_2

, compute

OO^\prime

Problem Statement