Point P lies on the diagonal AC of square ABCD with AP>CP. Let O1 and O2 be the circumcentres of △ABP and △CDP respectively. Given that AB=12 and ∠O1PO2=120∘, then AP=√a+√b, where a and b are positive integers. Find a+b. (correct answer + 5, wrong answer 0)

Point P lies on the diagonal AC of square ABCD with AP>CP. Let O1 and

1.	Point P lies on the diagonal AC of square ABCD with AP>CP. Let O1 and O2 be the circumcentres of △ABP and △CDP respectively. Given that AB=12 and ∠O1PO2=120∘, then AP=√a+√b, where a and b are positive integers. Find a+b. (correct answer + 5, wrong answer 0)
Answer» Point $P$ lies on the diagonal $A C$ of square $A B C D$ with $A P > C P .$ Let $O_{1}$ and $O_{2}$ be the circumcentres of $△ A B P$ and $△ C D P$ respectively. Given that $A B = 12$ and $∠ O_{1} P O_{2} = 120^{\circ},$ then $A P = \sqrt{a} + \sqrt{b},$ where $a$ and $b$ are positive integers. Find $a + b .$ (correct answer + 5, wrong answer 0)