Equal sum of distances in Poncelet configuration
Source: Sharygin geometry olympiad 2016, grade 10, Final Round, Problem 3.
August 5, 2016
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Problem Statement
Assume that the two triangles and have the common incircle and the common circumcircle. Let a point lie inside both the triangles. Prove that the sum of the distances from to the sidelines of triangle is equal to the sum of distances from to the sidelines of triangle .