Introduction to Tangents of a Circle

The video tutorial explores the concept of tangents to a circle, starting with their definition and origin. It discusses the properties of tangents, including their perpendicularity to the radius at the point of contact and the infinite number of tangents a circle can have. The tutorial provides geometric proofs to demonstrate these properties and explains the concept of parallel tangents. It also covers tangents drawn from an external point, proving their congruency using triangle congruence. The session concludes with a summary of the key properties of tangents.

What is the origin of the term 'tangent'?

• It was named after a famous circle.

• It comes from a Greek word meaning 'line'.

• It is a modern term with no historical origin.

• It is derived from a Latin word meaning 'to touch'.

How many tangents can a circle have?

• Two

• One

• Infinite

• Ten

What is always true about the angle between a radius and a tangent at the point of contact?

• It is 180 degrees.

• It is 90 degrees.

• It is 60 degrees.

• It is 45 degrees.

How many tangents can be parallel to a diameter of a circle?

• Two

• Three

• One

• Infinite

What happens when you try to draw a tangent from a point inside a circle?

• It becomes a secant.

• It becomes a diameter.

• It becomes a chord.

• It becomes a radius.

What is true about the lengths of tangents drawn from an external point to a circle?

• They are always different.

• They are always equal.

• One is always longer than the other.

• They depend on the circle's radius.

Which theorem can also be used to prove the equality of tangents from an external point?

• The Law of Sines

• Pythagoras' theorem

• The Angle Sum Property

• The Law of Cosines