# Online Geometry Problem 83. Area of a Excircle Contact Triangle, Exradius, Circumradius. Level: High School, College, Mathematics Education

 Given a triangle ABC of area S, the excircle of center D, the exradius ra, and the circumradius R. If Sa is the area of the contact triangle EFG, from the tangent points of the excircle and triangle ABC, prove that: .     "A great discovery solves a great problem, but there is a grain of discovery in the solution of any problem. Your problem may be modest, but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery. Such expert experiences at a susceptible age may create a taste for mental work and leave their imprint on mind and character for a lifetime." George Polya, 1944    HINTS: 1. See Proposed Problems 80, 81, 82.         CONTACT TRIANGLE: The contact triangle of a triangle ABC (figure above), also called the intouch triangle, is the triangle DEF formed by the points of tangency of the incircle of triangle ABC with triangle ABC.   AREA OF A TRIANGLE: Semiperimeter and Exradius Formula
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