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If a tangent and a chord intersect at a point on the circle, what is the relatio

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Question: If a tangent and a chord intersect at a point on the circle, what is the relationship between the angle formed and the angle subtended by the chord at the opposite arc?

Options:

  1. They are equal
  2. The tangent angle is double
  3. The chord angle is double
  4. They are supplementary

Correct Answer: They are equal

Solution: 

The angle formed by the tangent and the chord is equal to the angle subtended by the chord at the opposite arc.

If a tangent and a chord intersect at a point on the circle, what is the relatio

Practice Questions

Q1
If a tangent and a chord intersect at a point on the circle, what is the relationship between the angle formed and the angle subtended by the chord at the opposite arc?
  1. They are equal
  2. The tangent angle is double
  3. The chord angle is double
  4. They are supplementary

Questions & Step-by-Step Solutions

If a tangent and a chord intersect at a point on the circle, what is the relationship between the angle formed and the angle subtended by the chord at the opposite arc?
  • Step 1: Understand that a circle has a tangent line and a chord. A tangent touches the circle at one point, while a chord connects two points on the circle.
  • Step 2: Identify the point where the tangent and the chord intersect. This point is on the circle.
  • Step 3: Recognize that the angle formed between the tangent and the chord is called the 'tangent-chord angle.'
  • Step 4: Identify the arc opposite the chord. This is the part of the circle that does not include the chord.
  • Step 5: Understand that the angle subtended by the chord at the opposite arc is the angle formed by two lines drawn from the endpoints of the chord to any point on the opposite arc.
  • Step 6: The relationship states that the tangent-chord angle is equal to the angle subtended by the chord at the opposite arc.
  • Tangent-Chord Angle Theorem – The angle formed between a tangent and a chord through the point of contact is equal to the angle subtended by the chord at the opposite arc of the circle.
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