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If a tangent from point P touches a circle at point T, and the radius OT is 5 cm

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Question: If a tangent from point P touches a circle at point T, and the radius OT is 5 cm, what is the length of PT if PT is perpendicular to OT?

Options:

  1. 5√2 cm
  2. 5 cm
  3. 10 cm
  4. 25 cm

Correct Answer: 5 cm

Solution: 

Since PT is perpendicular to OT, PT is equal to the radius OT, which is 5 cm.

If a tangent from point P touches a circle at point T, and the radius OT is 5 cm

Practice Questions

Q1
If a tangent from point P touches a circle at point T, and the radius OT is 5 cm, what is the length of PT if PT is perpendicular to OT?
  1. 5√2 cm
  2. 5 cm
  3. 10 cm
  4. 25 cm

Questions & Step-by-Step Solutions

If a tangent from point P touches a circle at point T, and the radius OT is 5 cm, what is the length of PT if PT is perpendicular to OT?
  • Step 1: Understand that a tangent line touches the circle at only one point, which is point T in this case.
  • Step 2: Recognize that OT is the radius of the circle, and it measures 5 cm.
  • Step 3: Note that PT is a tangent line from point P to point T, and it is perpendicular to the radius OT.
  • Step 4: Since PT is perpendicular to OT, it means that PT forms a right angle with OT.
  • Step 5: In a right triangle formed by OT and PT, the length of PT is equal to the length of the radius OT.
  • Step 6: Therefore, the length of PT is also 5 cm.
  • Tangent and Radius Relationship – In a circle, a tangent at any point is perpendicular to the radius drawn to the point of tangency.
  • Properties of Right Triangles – Understanding the properties of right triangles can help in solving problems involving perpendicular lines.
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