MathDB

Points in a square [2011.II.13]

Source:

March 31, 2011

geometrycircumcircletrigonometrysymmetryinequalitiestrig identitiesLaw of Sines

Problem Statement

Point

P

lies on the diagonal

AC

of square

ABCD

with

AP>CP

. Let

O_1

and

O_2

be the circumcenters of triangles

ABP

and

CDP

respectively. Given that

AB=12

and

\angle O_1 P O_2 = 120^\circ

, then

AP=\sqrt{a}+\sqrt{b}

where

a

and

b

are positive integers. Find

a+b

.

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