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Inspheres and sum of angles

Source: Sharygin 2017 Day 2 Problem 10.6 Grade 10

August 2, 2017
geometry3D geometry

Problem Statement

10.6 Let the insphere of a pyramid SABCSABC touch the faces SAB,SBC,SCASAB, SBC, SCA at D,E,FD, E, F respectively. Find all the possible values of the sum of the angles SDA,SEB,SFCSDA, SEB, SFC.
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