Question

in the figure O is the centre of the circle. chords AB and CD are intersect at P. PC=4cm, PD=3cm, PO=2cm
(a) if the radius of the circle is taken as r what is the length of PB?
(b)PA×PB=
(c) what is the radius of the circle ​

Answer 1

Answer:

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.