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If a tangent and a chord intersect at a point on the circle, and the lengths of

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Question: If a tangent and a chord intersect at a point on the circle, and the lengths of the tangent and chord are 6 cm and 8 cm respectively, what is the angle between them?

Options:

  1. 30 degrees
  2. 45 degrees
  3. 60 degrees
  4. 90 degrees

Correct Answer: 90 degrees

Solution: 

The angle between a tangent and a chord at the point of contact is always 90 degrees.

If a tangent and a chord intersect at a point on the circle, and the lengths of

Practice Questions

Q1
If a tangent and a chord intersect at a point on the circle, and the lengths of the tangent and chord are 6 cm and 8 cm respectively, what is the angle between them?
  1. 30 degrees
  2. 45 degrees
  3. 60 degrees
  4. 90 degrees

Questions & Step-by-Step Solutions

If a tangent and a chord intersect at a point on the circle, and the lengths of the tangent and chord are 6 cm and 8 cm respectively, what is the angle between them?
  • Step 1: Understand that a tangent is a line that touches the circle at exactly one point.
  • Step 2: Recognize that a chord is a line segment whose endpoints lie on the circle.
  • Step 3: Identify the point where the tangent and the chord intersect on the circle.
  • Step 4: Remember the property that states the angle between a tangent and a chord at the point of contact is always 90 degrees.
  • Step 5: Conclude that the angle between the tangent and the chord is 90 degrees.
  • Tangent and Chord Theorem – The angle between a tangent and a chord drawn from the point of contact is always 90 degrees.
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