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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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
Transcribed Image Text: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
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