Understanding Circles and Tangents

What is the defining characteristic of a circle?

• It is a closed shape with no angles.

• All points are equidistant from a given point.

• It is a polygon with three sides.

• It has four equal sides.

Which of the following is a line segment with both endpoints on the circle?

• Tangent

• Secant

• Chord

• Radius

What is a diameter in relation to a circle?

• A segment with one endpoint at the center.

• A line that is perpendicular to the radius.

• A chord that passes through the center of the circle.

• A line that intersects the circle at one point.

How many points does a tangent line intersect a circle?

• Two points

• One point

• Three points

• No points

What is a common external tangent?

• A tangent that passes through the center of the circle.

• A tangent that intersects the segment joining the centers of two circles.

• A tangent that does not intersect the segment joining the centers of two circles.

• A tangent that is perpendicular to the radius.

According to the tangent line theorem, when is a line tangent to a circle?

• When it intersects the circle at two points.

• When it is a secant.

• When it is parallel to a radius.

• When it is perpendicular to a radius at the circle's edge.

How can you verify if a line is tangent to a circle using the Pythagorean theorem?

• By ensuring the sum of the squares of the two shorter sides equals the square of the longest side.

• By checking if the line is parallel to the radius.

• By measuring the angle between the line and the radius.

• By checking if the line passes through the center.

What is the value of x if RS = RT and RS = 28, RT = 3x + 4?

• x = 6

• x = 7

• x = 8

• x = 9

In a quadrilateral where each side is tangent to a circle, what can be said about the tangents from a common external point?

• They are parallel.

• They are perpendicular.

• They are congruent.

• They are unequal.

What is the perimeter of a quadrilateral with sides 6.4, 4.5, 6.4, and 8.3?

• 26.2

• 26.0

• 25.8

• 25.6