(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'