MathDB

In right triangle

ABC

with right angle at

C

\angle BAC < 45

degrees and AB \equal{} 4. Point

P

AB

is chosen such that \angle APC \equal{} 2\angle ACP and CP \equal{} 1. The ratio

\frac{AP}{BP}

can be represented in the form p \plus{} q\sqrt{r}, where

p,q,r

are positive integers and

r

is not divisible by the square of any prime. Find p\plus{}q\plus{}r.

Problem Statement