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Geometry-Circles

by Harshit
(New Delhi, India)










































I am not very good at geometry please help me with these questions :

a) PP' and QQ' are two direct tangents to two circles intersecting at points A and B. The common chord when produced intersect PP' at R and QQ' at S. Prove that RS(square)= PP'(square)+ AB (square).

b)Circle C (o,r) touches the circle C (o',r') internally at P. PB is a chord of larger circle , which intersect the smaller circle at A. Then prove that PA : PB =r : r'

c) Circles C (O,r) and C(O', r'), (r > r' ) touch internally at P. PQ is a chord of circle C (O,r) which intersect circle C (O' , r' ) at R. Show that OO'RQ is a Trapezium.

d)Two circles of radium r and r' touch externally at P. APB is a secant intersecting the circles respectively at A and B(other than P). Prove that PA/PB = r/r'

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