Question

In the given figure QR is a common tangent of the given circle touching at T meets QR at P . If PT = 3.8cm then find the length of QR(in cm)
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Answer 1

ANSWER :-

We have to find the Length of QR which is common tangent of the given circle (see the attachment) touching at T meets QR at P

For solving these problems we must know this given following property -

" Lengths of the tangents drawn from an external point to a circle are equal."

$Using \: this \: property, \: \\ We \: get \: to \: know \: that \\ PT = QP \: and \: \: PT = QR \\ So, \: QP = QR \\ \\ Given, \\ PT = 3.8 cm \\ \\ Now, \\ We \: can \: easily \: find \: QR \\ QR = QP + QR \\ \\ QR = [ 3.8 + 3.8 ] cm \\ \\ QR = 7.6 cm$

Hence,

The length of the tangent OR is 7.6 cm

Answer 2

Lengths of the tangents drawn from an external point to a circle are equal.

∴QP=PT=3.8cm..(i)

PR=PT=3.8cm..(ii)

From equations (i) and (ii):

QP=PR=3.8cm

But, QR=QP+PR

∴QR=3.8+3.8

QR=7.6cm

Therefore,

The length of the tangent QR is 7.6 cm

hope it is helpful..