MathDB

2020 Team #13

Source:

October 24, 2023

geometryteam test

Problem Statement

Let

ABCD

be a convex quadrilateral such that

\vartriangle ABC

is an equilateral triangle. Let

P

be a point inside the quadrilateral such that

\vartriangle APD

is an equilateral triangle and

\angle PCD = 30^o

. Suppose

CP = 6

and

CD = 8

. The area of the triangle formed by

P

, the midpoint of

\overline{BC}

, and the midpoint of

\overline{AB}

can be expressed in simplest radical form as

\frac{a+b\sqrt{c}}{d}

, where

a

,

b

,

c

, and

d

are positive integers with

gcd(a, b, d) = 1

and with

c

not divisible by the square of any prime. Compute

a + b + c + d

.

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