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Question

AB is the diameter of the circle with centre O. P is a point on the circle such that PA=2PB. If AB=d, find BP.


  1. √2d

  2. √5d

  3. 2√2d

  4. d/√5


Solution

The correct option is D

d/√5


Since, AB is the diameter,
APB=90

APB is a right angled triangle, right angled at P. So, by Pythagoras theorem,

AB2=AP2+PB2
=(2PB)2+PB2 
=5PB2
AB=5PB

PB=AB5=d5

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