Let ABC be an arbitrary triangle with side lengths a = |BC|, b = |CA|, and c = |AB|.

Let X, Y, and Z be the points of tangency of the incircle with the sides BC, CA, and AB respectively.

Let X', Y', and Z' be the points of tangency of the excircles with "sides" BC, CA, and AB respectively.

What is the value of |XX'| + |YY'| + |ZZ'| in terms of a, b, and c?
 

Edited on December 13, 2022, 10:02 pm

Posted by K Sengupta on 2022-12-13 22:00:45