Challenge 429: Twisted Triangles
These triangles might test your trigonometric talents!
Triangle ABC is equilateral with side length 14.
Triangle PQR is also equilateral with side length 4.
Triangle PQR is positioned inside triangle ABC such that A, P, Q lie on a straight line; B, Q, R lie on a straight line; C, R P lie on a straight line; and AP = BQ = CR.
What is the length AP?