MathDB

2017 PUMaC Team 6

Source:

September 19, 2019

geometry

Problem Statement

In regular pentagon

ABCDE

, let

O \in CE

be the center of circle

\Gamma

tangent to

DA

and

DE

.

\Gamma

meets

DE

at

X

and

DA

at

Y

. Let the altitude from

B

meet

CD

at

P

. If

CP = 1

, the area of

\vartriangle COY

can be written in the form

\frac{a}{b} \frac{\sin c^o}{\cos^2 c^o}

, where

a

and

b

are relatively prime positive integers and

c

is an integer in the range

(0, 90)

. Find

a + b + c

.

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