Geometry Problems, Online Education

Geometry Problem 158. Relation between the Circumradius, Inradius and Exradii of a triangle

In the figure below, ABC is a triangle inscribed in a circle of center O (circumcenter), I is the incenter and E1, E2, E3 are the excenters  relatives to the sides BC, AC, and AB respectively. Diameter DF of center O is perpendicular to AC at point E. If R, r, r1, r2, r3 are the circumradius, inradius and exradii respectively, (1) prove that Exradii proof, (2) prove that Exradius, Inradius Proof, and (3) prove that Circumradius, Inradius, Exradii Proof.

Triangle: circumradius, inradius, exradii

Geometric Art: Hyperbolic Kaleidoscope of problem 158 using iPad Apps.

Hyperbolic Kaleidoscope of problem 158 using iPad Apps

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