Question

find the length of the common external tangent to two circles of radius 18cm and 12 cm​

Answer 1

Answer:

Correct option is

A

24

Given−

ABIsthecommontangentoftwocircles,whotouch

eachother.

ABistheircommontangent.

ThecetreofonecircleisPwithradius=8cm

andthecetreofanothercircleisQwithradius=18cm.

Solution−

WejoinPQ,AP&PQ.

AperpendicularPNisdroppedfromPtoBQatN.

Now(AP&BQ)⊥ABsincetheradiusthroughthepoint

ofcontactofatangenttoacircleisperpendicular

tothetangent.

∴∠PAB=90  

o

=∠QBA.

Also∠PNB=∠PNQ=90  

o

sincePN⊥PQ.

∴ABNPisarectangle.

SoBN=AP=8cmandPN=AB.

∴NQ=BQ−BN=(18−8)cm=10cm.

AgainPQ=(8+18)cm=26cmsincethedistancebetweenthecentres

oftwocircles,touchingeachother,isthesumoftheirradii.

SoΔPNQisarighttrianglewithPQashypotenuse.

∴ByPythagorastheorem,weget

PN=  

PQ  

2

−NQ  

2

 

​

=  

26  

2

−10  

2

 

​

cm=24cm.

∴PN=AB=24cm.

Ans−OptionD.

Answer 2

Answer:

30

Step-by-step explanation:

we should do additional