Right Angle's Vertex Is On The Line!

Algebra Level 5

Suppose we have two points A(5,5)A(5, 5) and B(3,2)B(3, 2). Point C is placed on the line y=3x+4y = 3x+4 such that ABC\triangle ABC is a right triangle.

If CC has coordinates (x,y)(x, y) and the sum of all possible values of (x,y)(x, y) is PP, then find 11P11P.

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