Circle Tangents

What is the role of the radius in determining the properties of tangents?

• The radius determines the length of the tangent line only.

• The radius helps determine the angle of intersection with the tangent line and confirms the perpendicular relationship at the point of tangency.

• The radius has no effect on the properties of tangents.

• The radius is only relevant in circles with a diameter greater than one unit.

What is the difference between a secant line and a tangent line?

• A secant line intersects a circle at one point, while a tangent line intersects at two points.

• A secant line touches the circle at exactly one point, while a tangent line intersects at two points.

• A secant line intersects a circle at two points, while a tangent line touches the circle at exactly one point.

• A secant line is always longer than a tangent line.

How can you find the length of a tangent segment if you know the radius and the distance from the center to the external point?

• length = √(d² + r²)

• length = d - r

• length = √(d² - r²)

• length = d + r

What is the significance of the point of tangency?

• It is the only point where the tangent line touches the circle, defining the relationship between the circle and the tangent.

• It is the center of the circle where all radii meet.

• It is the point where two circles intersect each other.

• It is the point farthest from the center of the circle.

What is a tangent line to a circle?

• A line that intersects the circle at two points.

• A straight line that touches the circle at exactly one point, known as the point of tangency.

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

• A line that is parallel to the radius of the circle.

How do you calculate the perimeter of a circle?

• C = 2πr

• C = πd

• C = 2r

• C = r^2

What is the definition of a circle?

• A circle is a polygon with three sides.

• A circle is a set of points in a plane that are equidistant from a fixed point called the center.

• A circle is a closed figure with four equal sides.

• A circle is a shape that has no corners or edges.

How do you find the angle between a tangent and a radius?

• The angle is always 45 degrees.

• The angle is always 90 degrees.

• The angle is always 60 degrees.

• The angle is always 30 degrees.

What is the relationship between the angles formed by a tangent and a chord through the point of tangency?

• The angle formed between a tangent and a chord is equal to the angle in the opposite segment of the circle.

• The angle formed between a tangent and a chord is always 90 degrees.

• The angle formed between a tangent and a chord is equal to the sum of the angles in the adjacent segments.

• The angle formed between a tangent and a chord is equal to twice the angle in the opposite segment of the circle.

What is the relationship between a radius and a tangent line at the point of tangency?

• The radius drawn to the point of tangency is perpendicular to the tangent line.

• The radius is parallel to the tangent line at the point of tangency.

• The radius bisects the angle formed by the tangent line and the radius.

• The radius and the tangent line are equal in length.