Question

Two circle , one with centre M and radius 4 cm and the other with center N and radius 6 cm touch a line in P and Q respectively . M and N are on opposite sides of line PQ . If MN = 20 , find PQ

Answer 1

Answer:

using similarity triangle criteria

PN/QM=x/(20-x)

6/4=x/(20-x)

120-6x=4x

10x=120

x=12

20-x=20-12=8

using Pythagoras theorem

PO^2=12^2-6^2

=144-36=108

PO=6√3cm

similarly

OQ^2=8^2-4^2

=64-16=48

OQ=4√3

PQ=6√3+4√3

=10√3cm=17.32cm