MathDB

Nice Angles

Source: 2014 AIME II Problem #11

March 27, 2014

ratioanalytic geometrytrigonometrynumber theoryrelatively primePythagorean Theoremgeometry

Problem Statement

In

\triangle RED, RD =1, \angle DRE = 75^\circ

and

\angle RED = 45^\circ

. Let

M

be the midpoint of segment

\overline{RD}

. Point

C

lies on side

\overline{ED}

such that

\overline{RC} \perp \overline{EM}

. Extend segment

\overline{DE}

through

E

to point

A

such that

CA = AR

. Then

AE = \tfrac{a-\sqrt{b}}{c},

where

a

and

c

are relatively prime positive integers, and

b

is a positive integer. Find

a+b+c

.

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