# Playing with Pythagorean Triplets!

Geometry Level 5

A Primitive Pythagorean Triangle (PPT) is a right triangle whose sides have lengths which are integers, and have a greatest common divisor of 1. Among all pairs of non-congruent PPTs which have congruent incircles with an integer radius, let the pair for which this radius is minimized be $$(a_1, a_2, a_3)$$ and $$(b_1, b_2, b_3)$$, where $$a_1 < a_2 < a_3$$ and $$b_1 < b_2 < b_3$$. Find the value of $$a_1 + b_1 + a_2 + b_2 + a_3 + b_3$$?

×