Let ABCD be a convex quadrilateral, I and I2 be the incenters ofAABC and ADBC respectively. The line I Iz intersects the linesAB and DC at the points E and F respectively. Suppose lines ABPF. Prove that the points A, B,and DC intersect at P, and PE =C, Dare concyclic.

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Answered: Let ABCD be a convex quadrilateral, I…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Let ABCD be a convex quadrilateral, I and I2 be the incenters of AABC and ADBC respectively. The line I, I2 intersects the lines AB and DC at the points E and F respectively. Suppose lines AB and DC intersect at P, and PE = PF. Prove that the points A, B, C, Dare concyclic.