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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 |
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Answer» your answer is there please FOLLOW me and make me BRAIN list answer I HOPE this is helpful answer so make me brain list answer and please follow me 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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