From a point outside a circle, one tangent and one secant are drawn. The length of exterior part of secant is $7$ cm and that of interior part is $9$ cm. Find the length of tangent segment.

10.6

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10.9

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Solution

The correct option is A $10.6$ cm
Let length of tangent be $l$
Length of exterior part of secant $= m = 7$ cm
Length of interior part of secant $= n = 9$ cm
Now using the secant intersection theorem, we have
$l^{2} = m (m + n) \Rightarrow l^{2} = 7 (7 + 9) \Rightarrow l^{2} = 112$
$\Rightarrow l = \sqrt{112} = 10.6$ cm
Option A is correct.

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From a point outside a circle, one tangent and one secant are drawn. The length of exterior part of secant is 7 cm and that of interior part is 9 cm. Find the length of tangent segment.

The correct option is A 10.6 cmLet length of tangent be lLength of exterior part of secant =m=7 cmLength of interior part of secant =n=9 cmNow using the secant intersection theorem, we havel2=m(m+n)⇒l2=7(7+9)⇒l2=112⇒l=√112=10.6 cmOption A is correct.

From a point outside a circle, one tangent and one secant are drawn. The length of exterior part of secant is $7$ cm and that of interior part is $9$ cm. Find the length of tangent segment.