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Let A B C be a triangle right-angled at ...

Let `A B C` be a triangle right-angled at `Aa n dS` be its circumcircle. Let `S_1` be the circle touching the lines `A B` and `A C` and the circle `S` internally. Further, let `S_2` be the circle touching the lines `A B` and `A C` produced and the circle `S` externally. If `r_1` and `r_2` are the radii of the circles `S_1` and `S_2` , respectively, show that `r_1r_2=4` area `( A B C)dot`

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