Question

in the given circle O is the centre CD is the chord perpendicular to AB P is the meeting point PA=9cm PC = 6cm

1. What is the length of PD?

2. Find the length of PB?​

Answer 1

Answer:

a)AB and CD are two intersecting chords of the circle.

∴ Using circle chord property we can write

PC×PD=AP×PB

PC×PD=9×4=36cm  

2

 

(b) The product of PC and PD is 36.

Also AB is the diametre so PC+PD<AB=13cm

Only combination which will satisfy both of the above conditions is (6,6).

But for this combination PC=PD, which is possible only when CD⊥AB.

It is given in the question that CD is not perpendicular to AB.

There are no two other natural numbers whose product is 36 and sum is less than 13.

Hence PC and PD can not be natural numbers.