Chapter 9: Q2. (page 337)

Find $A B .$ In Exercise $3,$ $\bar{C B}$ is tangent to $⊙ A .$

Short Answer

Expert verified

The length of, $A B = 9 \sqrt{2}$ .

Step by step solution

Step 1. Given information.

The figure here given is,

Step 2. Concept Used.

$\cos A = \frac{leg adjacent to ∠ A}{hypotenuse}$

Step 3. Consider the given figure for further solution.

From the above figure it is clear that this triangle is a $45 {}^{\circ}- 45 {}^{\circ}- 90 °$ triangle.

So,

$m ∠ C A B = m ∠ C B A = 45$

Consider the right triangle $Δ O T J$ .

$\begin{matrix} \cos (C A B) = \frac{legadjacentto ∠ T O J}{hypotenuse} \\ \cos 45 ° = \frac{C A}{A B} \\ \frac{1}{\sqrt{2}} = \frac{9}{A B} \end{matrix}$

Step 4. Now perform cross multiplication.

$\begin{matrix} A B = 9 \times \sqrt{2} \\ A B = 9 \sqrt{2} \end{matrix}$

Therefore,the length of, $A B = 9 \sqrt{2}$ .

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Find $A B .$ In Exercise $3,$ $\bar{C B}$ is tangent to $⊙ A .$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept Used.

Step 3. Consider the given figure for further solution.

Step 4. Now perform cross multiplication.

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Find AB.In Exercise 3,CB¯ is tangent to ⊙A.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept Used.

Step 3. Consider the given figure for further solution.

Step 4. Now perform cross multiplication.

One App. One Place for Learning.

Most popular questions from this chapter

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Find $A B .$ In Exercise $3,$ $\bar{C B}$ is tangent to $⊙ A .$