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If a tangent to a circle makes a 30-degree angle with a chord drawn to the point

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Question: If a tangent to a circle makes a 30-degree angle with a chord drawn to the point of tangency, what is the measure of the angle between the chord and the radius at the point of tangency?

Options:

  1. 30 degrees
  2. 60 degrees
  3. 90 degrees
  4. 120 degrees

Correct Answer: 60 degrees

Solution: 

The angle between the chord and the radius at the point of tangency is equal to the angle between the tangent and the chord, which is 30 degrees. Therefore, the angle between the chord and the radius is 90 - 30 = 60 degrees.

If a tangent to a circle makes a 30-degree angle with a chord drawn to the point

Practice Questions

Q1
If a tangent to a circle makes a 30-degree angle with a chord drawn to the point of tangency, what is the measure of the angle between the chord and the radius at the point of tangency?
  1. 30 degrees
  2. 60 degrees
  3. 90 degrees
  4. 120 degrees

Questions & Step-by-Step Solutions

If a tangent to a circle makes a 30-degree angle with a chord drawn to the point of tangency, what is the measure of the angle between the chord and the radius at the point of tangency?
  • Step 1: Understand that a tangent to a circle touches the circle at exactly one point, called the point of tangency.
  • Step 2: Identify the angle formed between the tangent line and the chord drawn to the point of tangency. This angle is given as 30 degrees.
  • Step 3: Recall that at the point of tangency, the radius drawn to that point is perpendicular to the tangent line. This means the angle between the radius and the tangent is 90 degrees.
  • Step 4: To find the angle between the chord and the radius at the point of tangency, we can use the relationship between these angles.
  • Step 5: Since the angle between the tangent and the chord is 30 degrees, we can find the angle between the chord and the radius by subtracting the angle between the tangent and the chord from 90 degrees.
  • Step 6: Calculate the angle: 90 degrees - 30 degrees = 60 degrees.
  • Step 7: Conclude that the angle between the chord and the radius at the point of tangency is 60 degrees.
  • Tangent and Chord Angles – The relationship between the angles formed by a tangent line, a chord, and the radius at the point of tangency.
  • Angle Relationships in Circles – Understanding how angles relate to each other in the context of circles, particularly the right angle formed between the radius and the tangent.
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