If circles are inscribed inside the six triangles into which a triangle ABC is divided by its altitudes AD, BE, CF, then the sum of the diameters of these six circles together with the perimeter of the triangle ABC equals twice the sum of the altitudes of triangle ABC. Let O₁, O₂ be the inscribed Os of As ABD, ACD, touching BC, AD in G, P, H, Q. Join O₁G, O₂H, O₂P, O₂Q (Fig. 74). A B E PD 9₁ FIGURE 74

If circles are inscribed inside the six triangles into which a triangle ABC is divided by its altitudes AD, BE, CF, then the sum of the diameters of these six circles together with the perimeter of the triangle ABC equals twice the sum of the altitudes of triangle ABC. Let O₁, O₂ be the inscribed Os of As ABD, ACD, touching BC, AD in G, P, H, Q. Join O₁G, O₂H, O₂P, O₂Q (Fig. 74). A B E PD 9₁ FIGURE 74

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter7: Locus And Concurrence

Section7.2: Concurrence Of Lines

Problem 8E: a Is it really necessary to construct all three bisectors of the angles of a triangle to locate its...

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