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Standard X

Mathematics

Tangent

In the follow...

Question

In the following figure, ray PA is a tangent to the circle at A and PBC is a secant. If AP $= 15$ , BP= $10$ , then find BC.

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Solution

Ray $P A$ is a tangent and $P B C$ is a secant.

$∴ P A^{2} = P B \times P C$ … [Tangent secant property]

Given $P A = 15, P B = 10$

$∴ (15)^{2} = 10 \times P C$

$\Rightarrow 10 \times P C = 225$

$\Rightarrow P C = \frac{225}{10}$

$∴ P C = 22.5$

From the figure, $P B + B C = P C$

$∴ P B + B C = 22.5$

$\Rightarrow 10 + B C = 22.5$

$\Rightarrow B C = 22.5 - 10$

$∴ B C = 12.5$

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In the following figure, ray PA is a tangent to the circle at A and PBC is a secant. If AP=15, BP=10, then find BC.

Ray PA is a tangent and PBC is a secant.∴PA2=PB×PC … [Tangent secant property] Given PA=15,PB=10∴(15)2=10×PC ⇒10×PC=225⇒PC=22510∴PC=22.5 From the figure, PB+BC=PC∴PB+BC=22.5⇒10+BC=22.5⇒BC=22.5−10∴BC=12.5

In the following figure, ray PA is a tangent to the circle at A and PBC is a secant. If AP $= 15$ , BP= $10$ , then find BC.