Let ABC be a triangle and let P be a point inside. Let X, Y, Z be the intersections of AP, BP, CP with the sides BC, CA, AB, respectively. (a) Prove that: XB.YC ZA = √XB · XC · √YC YA· √ZA ZB.

Let ABC be a triangle and let P be a point inside. Let X, Y, Z be the intersections of AP, BP, CP with the sides BC, CA, AB, respectively. (a) Prove that: XB.YC ZA = √XB · XC · √YC YA· √ZA ZB.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

Chapter6: Circles

Section6.4: Some Constructions And Inequalities For The Circle

Problem 11E: X, Y, and Z are on circle O such that mXY=120, mYZ=130, and mXZ=110. Suppose that triangle XYZ is...

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Question

. Let ABC be a triangle and let P be a point inside. Let X, Y, Z be the intersections
of AP, BP, CP with the sides BC, CA, AB, respectively.
(a) Prove that:
XB YC ZA= √XB · XC √YC YA· √ZA · ZB.

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