Question

Two circles are given in a plane. State the conditions under which there is a common...

Two circles are given in a plane. State the conditions under which there is a common tangent line to both.
Explain how to construct the common tangent. Prove that your construction is correct.

Homework Answers

Answer #1

Conditions under which there is a common tangent line to both the circles are:

1. When two circles touch each other internally 1 common tangent can be drawn to the circles i.e.  |r1 - r2| = c1c2

2. When two circles intersect in two real and distinct points, 2 common tangents can be drawn to the circles i.e. |r1 - r2| < c1c2 < r1 + r2

3. When two circles touch each other externally, 3 common tangents can be drawn to the circles i.e.  r1 + r2 = c1c2

4. When two circle neither touch nor intersect and one lies outside the other, then 4 common tangents can be drawn i.e.  r1 + r2 < c1c2

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