Question

IF TWO CIRCLES WITH RADII 8 CM AND 3 CM RESPECTIVELY TOUCH INTERNALLY THEN FIND THE DISTANCE BETWEEN THEIR CENTRES

Answer 1

Step-by-step explanation:

Given−

Thecircles,C

1

wtthcentreO&ofradiusr

1

=8cmandC

2

wtthcentreP&ofradiusr

2

=3cm,toucheachother

internallyatQ.

(i)Toshowthat−

OP=r

1

−r

2

and

(ii)OP=r

1

−r

2

=?

Solution−

Weknowthatiftwocirclestouchinternallyatapointthenthe

pointofcontactandthecentresofthecircleslie

onthesamelinewhichcontainsthediametersof

thecircles.

(i)HerethepointofcontactisQ,

thecentreofC

1

isOandthatofC

2

isP.

∴ThelineSQcontainsthediametersofbothC

1

&C

2

.

i.eS,O,PandQlieonthesameline.

SoTheradiusofC

1

=r

1

isOQandtheradiusofC

1

=r

1

is

PQorPR.

∴ThedistancebetweenthecentresofC

OP=OQ−PQ=r

1

−r

2

(ii)OP=OQ−PQ=r

1

−r

2

=8cm−3cm=5cm.