Question: Let o1, o2 be circles inside an angle tangent to one of its sides in points A, B and to the other in points C, D. Prove that if o1, o2 are externally tangent, then ABCD has an inscribed circle.
What I have so far:
1.|AB| = |CD| by the strongest theorem of geometry
- A circle can be inscribed in a quadrilateral if and only if the addition of its opposite sides are equal ie. |AB|+|CD|=|BC|+|AD| (depends on how you label the vertices).
So we want to prove that 2|AB|=|BC|+|AD| and it must have to do with the circles being externally tangent.
I do not know how to proceed. Any help is much appreciated.