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(a) Prove the Power of a point theorem: Two intersecting lines cut a circle at points A, B and C,D respectively. If the lines intersect at P, then |PA| · |PB| = |PC| · |PD|. (b) State and prove the converse of the Power of point theorem. (c) Use part (b) to show that the vertices of any rectangle are co-circular.

(a) Prove the Power of a point theorem: Two intersecting lines cut a circle at points A, B and C,D respectively. If the lines intersect at P, then |PA| · |PB| = |PC| · |PD|. (b) State and prove the converse of the Power of point theorem. (c) Use part (b) to show that the vertices of any rectangle are co-circular.

Elementary Geometry For College Students, 7e
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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(a) Prove the Power of a point theorem: Two intersecting lines cut a circle at points A, B and C,D respectively. If the lines intersect at P, then |PA| · |PB| = |PC| · |PD|. (b) State and prove the converse of the Power of point theorem. (c) Use part (b) to show that the vertices of any rectangle are co-circular.
Transcribed Image Text:(a) Prove the Power of a point theorem: Two intersecting lines cut a circle at points A, B and C,D respectively. If the lines intersect at P, then |PA| · |PB| = |PC| · |PD|. (b) State and prove the converse of the Power of point theorem. (c) Use part (b) to show that the vertices of any rectangle are co-circular.
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