Understanding Tangents and Right Triangles

What is the condition for a line to be tangent to a circle?

• It must be longer than the radius.

• It must intersect the circle at exactly one point and be perpendicular to the radius.

• It must be parallel to the radius.

• It must pass through the center of the circle.

In the first example, what is the length of the hypotenuse when the radius is 12 and the other leg is 16?

• 18

• 20

• 22

• 24

Why is the line AB not tangent in the second example?

• Because the line is longer than the radius.

• Because the sum of the squares of the legs does not equal the square of the hypotenuse.

• Because the line does not intersect the circle.

• Because the line is parallel to the radius.

In the third example, what is the result of adding the squares of the legs 12 and 16?

• 450

• 400

• 350

• 300

What is the length of the unknown segment in the fourth example when the hypotenuse is 8.5?

• 8.5

• 5.5

• 6.5

• 7.5

In the fifth example, what is the length of the hypotenuse when the legs are 12 and 6.4?

• 16.6

• 15.6

• 13.6

• 14.6

What is the square of the hypotenuse in the example where the legs are 12 and 16?

• 300

• 450

• 350

• 400

In the final example, what is the length of the hypotenuse when the legs are 12 and 6.4?

• 12.6

• 14.6

• 13.6

• 15.6

What is the result of subtracting 2.25 from 6.25 in the example involving a radius of 1.5?

• 3

• 6

• 4

• 5

What is the square root of 400 in the example where the legs are 12 and 16?

• 18

• 19

• 21

• 20