Tan Chord Theorem Applications

The video tutorial explains the Tan Chord Theorem, a crucial concept in geometry often used in exams. It begins with drawing a circle and a tangent, followed by a chord that touches the tangent. The theorem states that the angle between the tangent and the chord is equal to any angle formed by the chord elsewhere on the circle. Euclid's findings are discussed, and multiple examples are provided to illustrate the theorem's application.

What is the first step in applying the tan chord theorem?

• Identify a tangent

• Locate the diameter

• Draw a triangle

• Find the center of the circle

Why is the tan chord theorem considered important?

• It is rarely used in exams

• It helps in finding the diameter

• It is not applicable to circles

• It is frequently used in exams

What must a chord do in relation to a tangent in the tan chord theorem?

• Pass through the center

• Start or end where the tangent touches the circle

• Be parallel to the tangent

• Intersect the tangent at two points

According to Euclid, what is the relationship between the angle formed by a tangent and a chord?

• It is unrelated to any other angle

• It is half of any other angle formed by the chord

• It is equal to any other angle formed by the chord

• It is always larger than any other angle

In the tan chord theorem, what is the significance of the angle between the tangent and the chord?

• It is always less than 30 degrees

• It is always 90 degrees

• It is equal to any angle formed by the chord

• It is the largest angle in the circle

What does the tan chord theorem help to determine?

• The length of the chord

• The equality of angles formed by the chord

• The radius of the circle

• The area of the circle

In the example given, if angle between tangent and chord is 50 degrees, what is the angle formed by the chord?

• 70 degrees

• 60 degrees

• 50 degrees

• 80 degrees

What is the angle formed by chord AC if the angle between tangent and chord is 60 degrees?

• 30 degrees

• 45 degrees

• 60 degrees

• 90 degrees

How does the tan chord theorem apply to different chords?

• It does not apply to any chord

• It only applies to chords parallel to the tangent

• It applies to any chord touching the tangent

• It only applies to chords passing through the center

What is the angle formed by chord BC if the angle between tangent and chord is 110 degrees?

• 120 degrees

• 110 degrees

• 100 degrees

• 90 degrees