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Relation between Inradius and Perimeter of Triangle

Lines are dra...

Question

Lines are drawn from the point $P (- 1, 3)$ to the circle $x^{2} + y^{2} - 2 x + 4 y - 8 = 0$ , which meets the circle at two points A and B. The minimum value of $P A + P B$ is

A

4

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B

6

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C

8

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D

16

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Solution

The correct option is D $8$
$P A + P B \geq 2 \sqrt{P A . P B}$ ...{A.M. $\geq$ G.M.}
$P A + P B \geq 2 P T$ ...by tangent-secant theorem
$P A + P B \geq 2 \sqrt{1 + 9 - (- 2) + 12 - 8} = 8$

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Relation between Inradius and Perimeter of Triangle

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