I is the incenter of a triangle ABC and the circumcircle of triangle BIC cuts AB, AC in D, E respectively. Show that (i) AB = AE and AC = AD. (ii) I is the orthocenter of the triangle formed by joining the circumcenters of As BIC, CIA, AIB. (iii) The circumcircle of ABC passes through the circumcenters of As BIC, CIA, AIB. Let P, Q, R be the circumcenters of As BIC, CIA, AIB respectively. Join IP, IQ, IR and produce them to meet the Os on BIC, CIA, AIB in F, G, H. Join FG, GH, HF, ID, IE, PB, PC

I is the incenter of a triangle ABC and the circumcircle of triangle BIC cuts AB, AC in D, E respectively. Show that (i) AB = AE and AC = AD. (ii) I is the orthocenter of the triangle formed by joining the circumcenters of As BIC, CIA, AIB. (iii) The circumcircle of ABC passes through the circumcenters of As BIC, CIA, AIB. Let P, Q, R be the circumcenters of As BIC, CIA, AIB respectively. Join IP, IQ, IR and produce them to meet the Os on BIC, CIA, AIB in F, G, H. Join FG, GH, HF, ID, IE, PB, PC

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

Chapter4: Quadrilaterals

Section4.3: The Rectangle, Square, And Rhombus

Problem 42E: a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three...

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