Question

The radii of two circles are 25 cm and 9 cm. The distance between their centres is 34 cm. Find the length of the common tangent segment to these circles. i want urent​

Answer 1

Answer:

Given−

AcirclewithcentreAandradius25cmexternallytouches

anothercirclewithcentreBandradius9cm.

PQistheircommontangent.

Tofindout−

ThelengthofPQ=?

Solution−

WejoinAP&BQ.

AlsoaperpedicularBLisdrawnfromBtoAP.

ItmeetsAPatL.

∴∠PLB=90

o

=∠ALB.

Also∠PQB=APQ=∠90

o

sincetheradiusthroughthepointof

contactofatangenttoacircleisperpendicularto

thetangent.

SoquadrilateralPLBQisarectangle.

∴PQ=LBandPL=BQ.

SoAL=AP−PL=(25−9)cm=16cm.

NowΔALBisarightonewithhypotenuseas

AB=(25+9)cm=34cm(sincethedistacebetweenthe

centresoftwocircles,touchingexternally,isthesum

oftheirradii.).

So,applyingPythagoratheorem,weget

LB= AB

2

−AL

=

34

2

−16

2

cm=30cm.

ButLB=PQ.

∴PQ=30cm.

Answer 2

Answer:

Step-by-step explanation:

Yo honey bro ohhh pra

Tha uppA ansa is correcta