MathDB

Find the lenght

Source:

May 16, 2015

geometrycircumcircle

Problem Statement

Given a acute triangle

PA_1B_1

is inscribed in the circle

\Gamma

with radius

1

. for all integers

n \ge 1

are defined:

C_n

the foot of the perpendicular from

P

to

A_nB_n

O_n

is the center of

\odot (PA_nB_n)

A_{n+1}

is the foot of the perpendicular from

C_n

to

PA_n

B_{n+1} \equiv PB_n \cap O_nA_{n+1}

If

PC_1 =\sqrt{2}

, find the length of

PO_{2015}

Cono Sur Olympiad - 2015 - Day 1 - Problem 3

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