Properties of Tangents Quiz

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

• It must be longer than the radius.

• It must be parallel to the radius.

• It must intersect the circle at two points.

• It must be perpendicular to the radius.

In Example 1, what theorem is used to verify if the line is tangent?

• The Law of Cosines

• The Pythagorean Theorem

• The Tangent-Secant Theorem

• The Law of Sines

In Example 1, what are the lengths of the sides of the triangle used in the Pythagorean theorem?

• 7, 24, 25

• 5, 12, 13

• 3, 4, 5

• 6, 8, 10

In Example 2, why is the line not tangent to the circle?

• The line is longer than the radius.

• The line intersects the circle at two points.

• The Pythagorean theorem does not hold true.

• The line is not perpendicular to the radius.

In Example 3, what is the purpose of using the Pythagorean theorem?

• To calculate the area of the circle

• To find the length of the radius

• To verify if the line is tangent

• To find the length of the tangent line

In Example 3, what is the length of the radius found using the Pythagorean theorem?

• 6

• 3

• 4

• 5

What is the property of tangents from a common external point?

• They are perpendicular.

• They are parallel.

• They are longer than the radius.

• They are congruent.

In the example with external tangents, what is the length of ED if FD is 3x + 4 and ED is 28?

• x = 7

• x = 9

• x = 8

• x = 6

What is the significance of the congruence of tangents from an external point?

• It helps in finding the radius.

• It helps in verifying tangency.

• It helps in solving for unknown variables.

• It helps in calculating the area of the circle.

In the context of tangents, what does it mean for two segments to be congruent?

• They have the same length.

• They are perpendicular.

• They are parallel.

• They intersect at the center.