Question

Two circles of radii 8 cm and 3 cm have their centres
13 cm apart. Find the length of a direct common
tangent to the two circles.

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Answer 1

PR=8Cm

SQ=3Cm

PQ=13Cm

Therefore, the length of AB=

$d = \sqrt{ {d}^{2} - ( R - {r})^{2} } \\ = \sqrt{ {13}^{2} - (8 - {3})^{2} } \\ = \sqrt{169 - {5}^{2} } \\ = \sqrt{169 - 25 } \\ = \sqrt{144} \\ = 12 \: \: \: cm$

The length of the direct tangent is 12 Cm.

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Answer 2

Answer:

$\implies$ The length of the direct tangent is 12cm.

$\large\underline\mathrm{Solution}$

PR = 8cm

SQ = 3cm

PQ = 13cm

Thus, the length of AB

$\implies$ d = √d² - (R - r)²

$\implies$ d = √13² - (8 - 3)²

$\implies$ d = √169 - (5)²

$\implies$ d = √169 - 25

$\implies$ d = √144

$\implies$ d = 12cm

$\implies$ The length of the direct tangent is 12cm.