Tangents to a Circle: Theorems

The video tutorial explains the properties of tangents to a circle, including the fact that a tangent touches the circle at exactly one point and is perpendicular to the radius at the point of contact. It discusses the theorem related to this property and explores how two tangents can be drawn from a point outside the circle. The tutorial further demonstrates that the lengths of these tangents are equal, using the concept of congruent triangles to prove this result.

What is the defining property of a tangent in relation to the circle?

• It intersects the circle at two points.

• It is parallel to the radius.

• It touches the circle at exactly one point.

• It is a secant line.

How many tangents can be drawn from a point outside a circle?

• Three

• One

• Four

• Two

What is the term used for the distance from an external point to the point of contact on the circle?

• Chord length

• Length of the tangent

• Diameter

• Radius

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

• They are unrelated.

• One is double the other.

• They are equal.

• They are always different.

Which geometric concept is used to prove the equality of tangent lengths from an external point?

• Similar triangles

• Pythagorean theorem

• Congruent triangles

• Parallel lines