Tangents and Secants

What is a tangent in a circle?

• A line that touches the circle at exactly one point

• A line that is parallel to the circle's diameter

• A line that intersects the circle at two points

• A line that passes through the center of the circle

How do you identify a secant in a circle?

• It intersects the circle at one point and one line

• It does not intersect the circle at all

• It intersects the circle at three distinct points

• It intersects the circle at two distinct points.

If the length of the tangent segment from a point outside the circle to the point of tangency is 8 cm, what is the radius of the circle?

• 12 cm

• 4 cm

• 16 cm

• 8 cm

Calculate the length of the tangent segment if the radius of the circle is 5 cm and the distance from the external point to the point of tangency is 12 cm.

• 13 cm

• 3 cm

• 20 cm

• 7 cm

If a secant segment and a tangent segment are drawn from an external point to a circle and the length of the secant segment is 10 cm, and the external point is 6 cm away from the circle, what is the length of the tangent segment?

• 12 cm

• 4 cm

• 5 cm

• 8 cm

What is the measure of an angle formed by a tangent and a secant if the tangent segment is 6 cm and the secant segment is 8 cm?

• 45 degrees

• 30 degrees

• 90 degrees

• 60 degrees

In a circle with a radius of 10 cm, a tangent is drawn at a point on the circle. If the length of the tangent segment is 12 cm, what is the distance between the point of tangency and the center of the circle?

• 20 cm

• 5 cm

• 15 cm

• 10 cm

A secant segment with a length of 15 cm is drawn to a circle with a radius of 6 cm. What is the distance between the center of the circle and the point where the secant intersects the circle?

• 3 cm

• 9 cm

• 12 cm

• 5 cm

If the measure of an angle formed by a tangent and a secant is 60 degrees, what is the measure of the intercepted arc by the secant?

• 180 degrees

• 90 degrees

• 120 degrees

• 30 degrees

A tree is 8 meters tall, and a person standing 2 meters away from the tree can see the top of the tree. What is the radius of the tree's base assuming the person's line of sight is a tangent to the tree?

• 4 meters

• 10 meters

• 6 meters

• 2 meters