Question

The centers of two circles are $41$ inches apart. The smaller circle has a radius of $4$ inches and the larger one has a radius of $5$ inches. The length of the common internal tangent is:

$41$ inches

$39$ inches

$39.8$ inches

$40.1$ inches

$40$ inches

Answer: E

Concepts:circles common internal tangent Pythagorean theorem

Difficulty rating: 1400

Small Hint:

For an internal common tangent, the perpendicular separation of the centers from the tangent is the sum of the radii

Big Hint:

Use a right triangle with hypotenuse $41$ and one leg $4+5$

Solution:

The center segment, the tangent segment, and a perpendicular leg of length $4+5=9$ form a right triangle. Thus the tangent length is $\sqrt{41^2-9^2}=\sqrt{1600}=40$ inches.

Thus, the correct answer is E.

1953 AMC 12 Problem 42

Answer: E

Difficulty rating: 1400

Small Hint:

Big Hint:

Solution:

Problem 42 in Other Years