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An acute triangle

ABC

is inscribed in a circle of radius 1 with centre

O;

all the angles of

ABC

are greater than

45^\circ.

B_{1}

is the foot of perpendicular from

B

CO,

B_{2}

is the foot of perpendicular from

B_{1}

AC.

Similarly,

C_{1}

is the foot of perpendicular from

C

BO,

C_{2}

is the foot of perpendicular from

C_{1}

AB.

The lines

B_{1}B_{2}

and

C_{1}C_{2}

intersect at

A_{3}.

The points

B_{3}

and

C_{3}

are defined in the same way. Find the circumradius of triangle

A_{3}B_{3}C_{3}.

Proposed by F.Bakharev, F.Petrov

Problem Statement