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I will make the assumption that P is on the circle
then if the centre is the origin , called O
then slope PO = -1/slope PA
y/x = -1/(y/(x-25) )
y/x = (25-x)/y
y^2 = 25x - x^2
but y^2 = 400 - x^2
400-x^2 = 25x - x^2
25x = 400
x = 16