Chapter 9: Q15. (page 336)

$\bar{P A}$ , $\bar{P B},$ and $\bar{R S}$ are tangents.
Explain, Why $P R + R S + S P = P A + P B .$

Short Answer

Expert verified

$P R + R S + S P = P A + P B$

Step by step solution

Step 1. Given information.

The figure here given is,

$\bar{P A}$ , $\bar{P B}$ and $\bar{R S}$ are tangents

Step 2. Concept Used.

Theorem $9.1$ Corollary,

Tangents to a circle from a point are congruent.

Step 3. Consider the given figure for further solution.

From the above figure,

it is clear that, $\bar{R A}$ and $\bar{R C}$ are tangents to the circle from the common point R,so by theorem $9.1$ corollary, it can be said that,

$R A = R C$ ….. (1)

Similarly, $\bar{B S}$ and $\bar{C S}$ are tangents to the circle from the common point \[S\],so by theorem $9.1$ corollary, it can be said that,

$B S = C S$ ….. (2)

Now consider,

$P A + P B = P R + R A + B S + S P$

Then using $(1)$ and $(2)$ ,

$\begin{matrix} P A + P B = P R + R C + C S + S P \\ = P R + (R C + C S) + S P \\ = P R + R S + S P \end{matrix}$

Therefore, it is proved that, $P R + R S + S P = P A + P B$ .

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$\bar{P A}$ , $\bar{P B},$ and $\bar{R S}$ are tangents.
Explain, Why $P R + R S + S P = P A + P B .$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept Used.

Step 3. Consider the given figure for further solution.

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PA¯, PB¯,and RS¯ are tangents.Explain, Why PR+RS+SP=PA+PB.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept Used.

Step 3. Consider the given figure for further solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

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$\bar{P A}$ , $\bar{P B},$ and $\bar{R S}$ are tangents.
Explain, Why $P R + R S + S P = P A + P B .$