f the distances from the origin of the centers of three circles x\power{2}+y\power{2}+2?\index{i}x-c=0,(i=1,2,3),are in GP,then prove that the lengths of the tangents drawn to them from any point on the circle x\power{2}+y\power{2}=c\power{2} are in GP

f the distances from the origin of the centers of three circles x\power{2}+y\power{2}+2?\index{i}x-c=0,(i=1,2,3),are in GP,then prove that the lengths of the tangents drawn to them from any point on the circle x\power{2}+y\power{2}=c\power{2} are in GP

Elementary Geometry for College Students

6th Edition

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Daniel C. Alexander, Geralyn M. Koeberlein

Chapter7: Locus And Concurrence

Section7.CT: Test

Problem 5CT: Describe the locus of points in space that are at a distance of 3 cm from point P....

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Question

If the distances from the origin of the centers of three circles x\power{2}+y\power{2}+2?\index{i}x-c=0,(i=1,2,3),are in GP,then prove that
the lengths of the tangents drawn to them from any point on the circle x\power{2}+y\power{2}=c\power{2} are in GP.

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