Geography, asked by aliasbumet3574, 6 months ago

A circle of radius 2cm Touches a circle of radius 10 cm internally. Determine the length of a tangent segment drawn through the center of the larger circle to smaller circle

Answers

Answered by Niara72
0

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Answer:

Given−

AcircleC

1

ofradius5cmtouchesanotherbiggercircle

C

2

internallyatA.

C

1

passesthroughthecentreMofC

2

.

ThetangentCDtouchesC

1

atP.

CDmeetsC

2

atD.

Tofindout−

CD=?

Solution−

ADisjoined.

CAisthediameterofC

2

sinceNisthecentreofC

2

.

NowAN=2MN=2×5cm=10cm

ButCN=AN(radiiofthesamecircle).

SoCN=10cmandCM=CN+MN=(10+5)cm=15cm.

AlsoCA=2×AN=2×10cm=20cm.

Again∠CPM=90

o

sincetheradius,meetingthepoint

ofcontactofthetangenttoacircle,makes90

o

angle

withthetangent.

∴ΔCPMisarightonewithCMashypotenuse.

∴CP=

CM

2

−PM

2

=

15

2

−5

2

cm=10

2

cm.

Also∠ADC=90

o

sinceitisanangleinthesemicircle.

∴ΔADCisarightonewithCAashypotenuse

(applyingPythagorastheorm).

NowbetweenΔADC&ΔCPMwehave

∠ADC=90

o

=∠CPM,∠MCPcommon.

∴ΔADC&ΔCPMaresimilar.

i.e

CA

CD

=

CM

CP

⟹CD=

CM

CP

×CA=

15

10

2

×20cm

⟹CD=

3

40

2

cm.

Ans−OptionD.

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