Question

How many common internal tangents can be drawn to each pair of circles in exercise 1 above ?

Short answer

a. The final answer is $2.$

b.The final answer is $1.$

c.The final answer is $0.$

d.The final answer is $0.$

e.The final answer is $0.$

f.The final answer is $0.$

Step-by-step solution

Part a. Step 1. Given information:

The figure is given.

Step 2. Concept use.

A tangent is internal tangent if the intersection of tangent and line joining centres of two circles is empty.

Step 3.  Applying the concept.    

Now, we apply our concept that is-

A tangent is internal tangent if the intersection of tangent and line joining centres of two circles is empty.

Given figure has two internal tangents as shown below.

Therefore, the answer is $2.$

Part b. Step 1. Given information:

The figure is given.

Step 2. Concept use.

A tangent is internal tangent if the intersection of tangent and line joining centres of two circles is empty.

Step 3.  Applying the concept.    

Now, we apply our concept that is-

A tangent is internal tangent if the intersection of tangent and line joining centres of two circles is empty.

Given figure has two internal tangents as shown below.

Therefore, the answer is $1.$

Part  c. Step 1. Given information:

The figure is given.

Step 2. Concept use.

A tangent is internal tangent if the intersection of tangent and line joining centres of two circles is empty.

Step 3.  Applying the concept.    

Now, we apply our concept that is-

A tangent is internal tangent if the intersection of tangent and line joining centres of two circles is empty.

Given figure has no internal tangents.

Therefore, the answer is $0.$

Part  d. Step 1. Given information:

The figure is given.

Step 2. Concept use.

A tangent is internal tangent if the intersection of tangent and line joining centres of two circles is empty.

Step 3.  Applying the concept.    

Now, we apply our concept that is-

A tangent is internal tangent if the intersection of tangent and line joining centres of two circles is empty.

The figure has no internal tangents.

Therefore, the answer is $0.$

Part e. Step 1. Given information:

Step 2. Concept use.

A tangent is internal tangent if the intersection of tangent and line joining centres of two circles is empty.

Step 3.  Applying the concept.    

Now, we apply our concept that is-

A tangent is internal tangent if the intersection of tangent and line joining centres of two circles is empty.

The figure has no internal tangents.

Therefore, the answer is $0.$

Part f. Step 1. Given information:

The figure is given.

Step 2. Concept use.

A tangent is internal tangent if the intersection of tangent and line joining centres of two circles is empty.

Step 3.  Applying the concept.    

Now, we apply our concept that is-

A tangent is internal tangent if the intersection of tangent and line joining centres of two circles is empty.

The figure has no common tangent.

Therefore, the answer is $0.$