Let AB = a and AC = b
A^2 + b^2 = 400 by pythagoras
Let AP = x and BP = y, so CP= 20-y
So, by Pythagoras
X^2 + y^2 = a^2 and b^2 = x^2 + (20-y)^2
Maximum possible value of AP occurs when a = b, so a= b=10 root 2
On solving, we get AP = 10 units
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