Question

a. Which pair of circles shown above are externally tangent?

b. Which pair are internally tangent?

Short answer

a. The final answer is $b.$

b. The final answer is $\left(e\right).$

Step-by-step solution

Part a. Step 1. Given information:

The figure is given.

Step 2. Concept use.

Two circles are externally tangent if their intersection point is one and intersection of their interior is empty.

Step 3. Applying the concept.    

Now, we apply our concept that is-

Two circles are externally tangent if their intersection point is one and intersection of their interior is empty.

Therefore in figure (b) pair of circles are externally tangents as shown below.

Given figure has two internal tangents as shown below.

Therefore, the answer is $\left(b\right).$

Part b. Step 1. Given information:

The figure is given.

Step 2. Concept use.

Two circles are externally tangent if their intersection point is one and intersection of their interior is not empty.

Step 3.  Applying the concept.    

Now, we apply our concept that is-

Two circles are externally tangent if their intersection point is one and intersection of their interior is not empty.

Therefore in figure (b) pair of circles are internally tangents as shown below.

Therefore, the answer is $e.$