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area of K_aK_bK_c does not exceed that of ABC, mixtilinears related

Source: Mathley 2014.2 p2

August 20, 2020
mixtilineargeometryareasgeometric inequality

Problem Statement

Let ABCABC be a triangle with a circumcircle (K)(K). A circle touching the sides AB,ACAB,AC is internally tangent to (K)(K) at KaK_a; two other points Kb,KcK_b,K_c are defined in the same manner. Prove that the area of triangle KaKbKcK_aK_bK_c does not exceed that of triangle ABCABC.
Nguyen Minh Ha, Hanoi University of Education, Xuan Thuy, Cau Giay, Hanoi.
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