MathDB

In isosceles triangle

ABC

A

is located at the origin and

B

is located at

(20, 0)

. Point

C

is in the first quadrant with

AC = BC

and

\angle BAC = 75^\circ

. If

\triangle ABC

is rotated counterclockwise about point

A

until the image of

C

lies on the positive y-axis, the area of the region common to the original and the rotated triangle is in the form

p\sqrt{2}+q\sqrt{3}+r\sqrt{6}+s

where

p

q

r

s

are integers. Find

(p-q+r-s)/2

Problem Statement