Math Problem Statement

A triangle ABC is assumed with the orthocenter H and incenter I. We have chosen the point K so that AK+AH=BK+BH=CK+CH. Prove I,K and H are collinear.

Solution

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Math Problem Analysis

Mathematical Concepts

Triangle Geometry
Isogonal Conjugates
Incircle and Circumcircle

Formulas

AK + AH = BK + BH = CK + CH

Theorems

Isogonal Conjugate Property
Exsimilicenter Property

Suitable Grade Level

Undergraduate