Question

If ab is the diameter of the circlre,the chord cd is perpendicular to ab intersecting at p.if cp=2cm and pb =1,what is the radius of the circle?

Answer 1

Given : AB is the diameter of the circle, the chord CD  is perpendicular to AB intersecting at P.  

CP=2cm and PB  =1 cm

To Find : radius of the circle

Solution:

AB is the diameter of the circle

=> AB = 2R

R is radius

PB = 1 cm

=> PA = 2R - 1   cm

Chord CD is perpendicular to Diameter (AB)

Hence CP = DP  = 2 cm

PA * PB  = CP * DP

=> 1 (2R - 1)  = 2 * 2

=> 2R - 1 = 4

=> 2R = 5

=> R = 5/2

=> R = 2.5 cm

radius of the circle is 2.5 cm

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