Chapter 9: Q4. (page 335)

Given $\bar{P A}$ and $\bar{P B}$ are tangents to $⊙ o .$
Use the diagram at the right to explain how the corollary on page $333$
follows from Theorem $9 - 1 .$

Short Answer

Expert verified

a. Tangent $P A$ is congruent to tangent $P B .$

Step by step solution

Step 1. Given information:

The figure is given.

Step 2. Concept used:

We used the theorem 9-1.

Step 3. Applying the concept:

If the line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangents.

Then,

$\begin{array}{l} O A ⊥ P A \\ O B ⊥ P B \end{array}$

Then once can say that,

$\begin{array}{l} ∠ P A O = 90^{\circ} \\ ∠ P B O = 90^{\circ} \end{array}$
It is required to prove two triangles are congruent.

Consider in $▵ P A O$ and $▵ P B O,$

$\begin{array}{l} O A = O B \\ ∠ P A O = ∠ P B O \\ P O = O P \end{array}$

(Radius of a circle is equal)

(Both the angles are )

(Common side of a triangle)

So, it implies that

$▵ P A O ≅ ▵ P B O$ ( Side-Angle-Side Rule)

Since the corresponding parts of congruent triangles are congruent.

Therefore, the following holds good $P A$ and $P B .$

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Given $\bar{P A}$ and $\bar{P B}$ are tangents to $⊙ o .$
Use the diagram at the right to explain how the corollary on page $333$
follows from Theorem $9 - 1 .$

Short Answer

Step by step solution

Step 1. Given information:

Step 2. Concept used:

Step 3. Applying the concept:

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Given PA¯and PB¯ are tangents to ⊙o.Use the diagram at the right to explain how the corollary on page 333follows from Theorem9-1.

Short Answer

Step by step solution

Step 1. Given information:

Step 2. Concept used:

Step 3. Applying the concept:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Mechanics Maths

Decision Maths

Applied Mathematics

Discrete Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

Given $\bar{P A}$ and $\bar{P B}$ are tangents to $⊙ o .$
Use the diagram at the right to explain how the corollary on page $333$
follows from Theorem $9 - 1 .$