In a right triangle ACB show that the incircle touches sides AC and CB in points that are vertically lined up with the centers of the incircles for ADC and BDC. Furthermore, show that the red and green distances are equal.

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## Solution

Three similar triangles with their incircles so all measurements are proportional, in particular distance of tangency points from vertices, so XY is parallel to CD and is a diameter etc. Also proportions of the two smaller triangles show equality of red and green.