Chapter 9: Q7. (page 336)

$(a) .$ What do you think is true of common external tangents $\bar{A B}$ and $\bar{C D}$ $?$ prove it.
$(b) .$ Will your results in part $(a)$ be true if the circles are congruent $?$

Short Answer

Expert verified

(a)

The tangent $A B$ is congruent to tangent $C D$ .

Step by step solution

Step 1. Given information.

The figure here given is,

Step 2. Concept used.

In the given figure, $B Z$ and $D Z$ are tangents.

If circle has a two tangent from a unique point then there are equal,

$B Z = D Z$ and $A Z = C Z . . . . . . . . (1)$

The sum of $B A$ and $A Z$ is $D Z$

Step 3. This implies as shown below.

$\begin{array}{l} B Z = D Z \\ B A + A Z = D C + C Z \end{array}$

It is known that $A Z = C Z$ from (1)

Subtract $A Z$ from both sides to get,

$B A = D C$

Therefore, it is proved that $A B ≅ C D$ .

$(b)$

Yes, the results in part $(a)$ holds good if the circles are congruent.

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$(a) .$ What do you think is true of common external tangents $\bar{A B}$ and $\bar{C D}$ $?$ prove it.
$(b) .$ Will your results in part $(a)$ be true if the circles are congruent $?$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. This implies as shown below.

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a.What do you think is true of common external tangents AB¯and CD¯?prove it.b.Will your results in part abe true if the circles are congruent?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. This implies as shown below.

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

$(a) .$ What do you think is true of common external tangents $\bar{A B}$ and $\bar{C D}$ $?$ prove it.
$(b) .$ Will your results in part $(a)$ be true if the circles are congruent $?$