$( A) \ 3.8$
$( B) \ 76$
$( C) \ 5.7$
$( D) \ 1.9$"
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In Fig. 1, QR is a common tangent to the given circles, touching externally at the point. The tangent at T meets QR at P. If $PT= 3.8\ cm$, then the length of QR $( in\ cm)$ is:

$( A) \ 3.8$
$( B) \ 76$
$( C) \ 5.7$
$( D) \ 1.9$"

Given: In Fig. 1, QR is a common tangent to the given circles, touching externally at the point. The tangent at T meets QR at P. And $PT=3.8\ cm$.

To do: To find the length of $QR( in\ cm)$ .

Solution:

As known that the length of the tangents drawn from an external point to a circle is equal 

$QP=PT=3.8\ cm\ ...................( 1)$

$PR=PT=3.8\ cm......................\ ( 2)$ 

From equations $( 1)$ and $( 2)$, we get: 

$QP=PR=3.8\ cm$

Now, $QPR=QP+PR=3.8\ cm\ +\ 3.8\ cm=7.6\ cm$

Hence, the correct option is $( B)$.

 

Updated on: 10-Oct-2022

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