Question

Two circles intersect at two points. Which of the following statements is true?

• A. The internal tangent is longer than the external tangent
• B. Only two common tangents exist
• C. The number of tangents depends on radii
• D. They must be concentric

Answer 1

Answer:

B. Only two common tangents exist

When two circles intersect at two distinct points, they have exactly two common tangents, and both are external tangents. There are no internal common tangents because the circles overlap.

Therefore:

• ❌ The internal tangent is longer than the external tangent.

• ✅ Only two common tangents exist.

• ❌ The number of tangents depends on radii.

• ❌ They must be concentric.

Answer:

$\boxed{\text{Only two common tangents exist.}}$