There is an incircle of triangle ABC. Two circles touch this incircle and sides of the triangle.

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There is an incircle of triangle ABC. Two circles touch this incircle and sides of the triangle. Find the ratio of radii of the two circles.
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AWESOME example.
I thought I wouldn't be able to solve for radii using similar triangles, so I used Homothety instead.
Thanks A LOT.

triathlon.