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If a tangent touches a circle at point A and a line from the center to point A i

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Question: If a tangent touches a circle at point A and a line from the center to point A is drawn, what is the angle between the tangent and the radius?

Options:

  1. 0 degrees
  2. 45 degrees
  3. 90 degrees
  4. 180 degrees

Correct Answer: 90 degrees

Solution: 

The tangent to a circle at any point is perpendicular to the radius drawn to the point of contact, hence the angle is 90 degrees.

If a tangent touches a circle at point A and a line from the center to point A i

Practice Questions

Q1
If a tangent touches a circle at point A and a line from the center to point A is drawn, what is the angle between the tangent and the radius?
  1. 0 degrees
  2. 45 degrees
  3. 90 degrees
  4. 180 degrees

Questions & Step-by-Step Solutions

If a tangent touches a circle at point A and a line from the center to point A is drawn, what is the angle between the tangent and the radius?
  • Step 1: Understand that a tangent is a line that touches the circle at exactly one point.
  • Step 2: Identify the point where the tangent touches the circle. Let's call this point A.
  • Step 3: Draw a line from the center of the circle to point A. This line is called the radius.
  • Step 4: Recognize that the tangent line and the radius meet at point A.
  • Step 5: Remember the property of tangents: the tangent line is always perpendicular to the radius at the point of contact.
  • Step 6: Since perpendicular lines form a right angle, the angle between the tangent and the radius at point A is 90 degrees.
  • Tangent and Radius Relationship – The tangent to a circle at any point is always perpendicular to the radius drawn to the point of contact.
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