circle circle everywhere

Geometry Level pending

Let ABC be a triangle with angle A=90degree , and "S" be its circumcircle. Let "S1" be the circle touching the rays AB , AC and the circle S internally . further let "S2" be the circle touching the rays AB, AC and the circle "S" externally . if r1 , r2 be the radii of the circles "S1" and "S2" respectively , then

r1r2= P [ABC]

{hint = P is a positive integer }

[ABC] means area of triangle ABC.

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