Question

The distance between the centers of two circles of radius 7.5 cm and 2.5 cm is 19 cm. What is the length (in cm) of transverse common tangent?​

Answer 1

$\bf{\underline{\underline{Question}}}$

The distance between the centers of two circles of radius 7.5 cm and 2.5 cm is 19 cm. what is the length (in cm) of transverse common tangent?

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$\bf{\underline{\underline{Answer -}}}$

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$\bf\fbox{\underline\green{Given-}}$

ㅤㅤ ㅤㅤㅤ ㅤㅤRadius(R1) =7.5cm

ㅤㅤ ㅤㅤㅤ ㅤㅤRadius(R2) =2.5cm

Distance between centre of ㅤㅤ ㅤㅤㅤ ㅤㅤㅤㅤ ㅤㅤㅤ ㅤㅤcircle= 19cm

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$\bf{\underline{\underline{Solution}}}$

The length(in cm) of transverse common tangent

$\bf{ \sqrt{( {(distane \: between \: the \: centre \: of \: circle}^{2} - {(R1-R2)}^{2} } }$

1$= \bf{ \sqrt{( {19)}^{2} - {10}^{2}} }$

$= \bf{ \sqrt{ {361 - \: {10}^{2}}} }$

$= \bf{ \sqrt{361 - 100} }$

$= \bf{ 19 - 10 }$

$\bf\fbox{9 cm}$

$\bf\red{\underline{The \: length (in cm) \: of \: transverse \: common \: tangent \: is \: \: cm}}$