Question

How many common external tangents can be drawn to the two circles?

Short answer

a. The final answer is $2.$

b. The final answer is $2.$

c. The final answer is $2.$

d. The final answer is $2.$

e. The final answer is $1.$

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

Given figure has two external 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 external 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 external tangent if the intersection of tangent and line joining centres of two circles is empty.

Given figure has two external tangents as shown below.

Therefore, the answer is $2.$

Part c. Step 1. Given information:

The figure is given.

Step 2. Concept use.

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

Given figure has two external tangents as shown below.

Therefore, the answer is $2.$

Part d. Step 1. Given information:

The figure is given.

Step 2. Concept use.

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

Given figure has two external tangents as shown below.

Therefore, the answer is $2.$

Part e. Step 1. Given information:

The figure is given.

Step 2. Concept use.

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

Given figure has two external tangents as shown below.

Therefore, the answer is $1.$

Part f. Step 1. Given information:

The figure is given.

Step 2. Concept use.

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

Below figure has no common tangent.

Therefore, the answer is $0.$