-9 cm - CP -4 cm and TP is a tangent at T- Find PT-A- 2 cmB- 6 cmC- 9 cmD- 8 cm

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Intersection between Tangent and Secant

=9 cm , CP =4...

Question

In the above given figure, PB = 9 cm, CP = 4 cm and TP is a tangent at T. Find PT.

6 cm

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9 cm

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8 cm

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2 cm

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Solution

The correct option is A
6 cm

Given: CP = 4 cm, PB = 9 cm and TP is a tangent at point T.

We know that, if a chord and a tangent intersect externally, then the product of the lengths of the segments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection
i.e. $(P C) \times (P B) = (P T)^{2} \Rightarrow 4 \times 9 = (P T)^{2} \Rightarrow 36 = (P T)^{2} \Rightarrow \sqrt{36} = P T$
$∴$ PT = 6

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