Tangent Lines and Circle Properties

This video tutorial covers the concept of tangents to a circle, explaining that a tangent is a line that intersects a circle at only one point. It discusses the properties of tangents, including the fact that there is only one tangent at a given point on a circle and that tangents from an external point are equal in length. The tutorial provides a proof using congruent triangles to show the equality of tangent lengths and demonstrates how to calculate the length of a tangent using the Pythagorean theorem.

What is a tangent to a circle?

• A line that is parallel to the circle

• A line that intersects the circle at only one point

• A line that intersects the circle at two points

• A line that does not touch the circle

How many tangents can be drawn at a single point on a circle?

• None

• Two

• Three

• One

What is the relationship between two tangents drawn from an external point to a circle?

• They are perpendicular

• They intersect at the center

• They are equal in length

• They are parallel

Which rule is used to prove the equality of tangents in the given lesson?

• SAS Rule

• SSS Rule

• RHS Rule

• ASA Rule

What is the common side in the congruent triangles used in the proof?

• RP

• PQ

• OP

• OR

What theorem is used to find the length of a tangent?

• Euclid's Theorem

• Thales' Theorem

• Pythagorean Theorem

• Fermat's Theorem

If the radius of a circle is 8 cm and the distance from the center to an external point is 17 cm, what is the length of the tangent?

• 17 cm

• 15 cm

• 10 cm

• 8 cm

What is the value of OP squared in the example problem?

• 64

• 256

• 289

• 225

What is the length of the tangent if the radius is 8 cm and the distance from the center is 17 cm?

• 15 cm

• 10 cm

• 18 cm

• 12 cm

What is the square root of 225?

• 18

• 12

• 10

• 15