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If a tangent from point P touches the circle at point T, and the radius OT is 6

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Question: If a tangent from point P touches the circle at point T, and the radius OT is 6 cm, what is the length of PT if PT is the tangent?

Options:

  1. 6 cm
  2. 12 cm
  3. 8 cm
  4. 10 cm

Correct Answer: 6 cm

Solution: 

The length of the tangent PT from point P to the point of tangency T is equal to the radius OT, which is 6 cm.

If a tangent from point P touches the circle at point T, and the radius OT is 6

Practice Questions

Q1
If a tangent from point P touches the circle at point T, and the radius OT is 6 cm, what is the length of PT if PT is the tangent?
  1. 6 cm
  2. 12 cm
  3. 8 cm
  4. 10 cm

Questions & Step-by-Step Solutions

If a tangent from point P touches the circle at point T, and the radius OT is 6 cm, what is the length of PT if PT is the tangent?
  • Step 1: Understand that a tangent is a line that touches a circle at exactly one point.
  • Step 2: Identify the point where the tangent touches the circle, which is point T in this case.
  • Step 3: Recognize that the radius of the circle at point T is OT, which is given as 6 cm.
  • Step 4: Know that the length of the tangent PT from point P to point T is equal to the radius OT.
  • Step 5: Therefore, the length of PT is also 6 cm.
  • Tangent to a Circle – A tangent to a circle is a line that touches the circle at exactly one point, and the radius drawn to the point of tangency is perpendicular to the tangent.
  • Properties of Tangents – The length of a tangent from an external point to a circle is equal to the square root of the difference between the square of the distance from the external point to the center of the circle and the square of the radius.
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