Bending A Triangle

Geometry Level 2

Triangle ABC ABC has coodinates A=(4,0)A= (-4, 0), B=(4,0)B= (4 , 0), and C=(0,3)C= (0 , 3).

Let PP be the point in the first quadrant such that ABP\triangle ABP has half the area of ABC\triangle ABC but both triangles have the same perimeter.

What is the length of CP?CP? If your solution is in a form of d\sqrt{d}, submit dd as the answer.

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