Question

For a circle with centre O and radius 5 cm, which of the following statements is true?
P: Distance between every pair of parallel tangents is 10 cm.
Q: Distance between every pair of parallel tangents must be between 5 cm and 10 cm.
R: Distance between every pair of parallel tangents is 5 cm.
S: There does not exist a point outside the circle from where length of tangent is 5 cm.

• A. Q
• B. P
• C. R
• D. S

Hint:

In circles, parallel tangents can vary in distance based on location but never less than radius or more than diameter.

Answer 1

The Correct Option is B

Given:
A circle with center \(O\) and radius = 5 cm

We will now evaluate statements P, Q, R, and S.

Statement P: Distance between any pair of parallel tangents is 10 cm.
✔️ True.
Explanation: Parallel tangents are separated by the diameter. Since radius = 5 cm, diameter = \(2 \times 5 = 10\) cm. Therefore, the distance between parallel tangents is 10 cm.

Statement Q: Distance between any pair of parallel tangents must be between 5 cm and 10 cm.
❌ False.
Explanation: As shown above, the distance is precisely 10 cm, not a range.

Statement R: Distance between any pair of parallel tangents is 5 cm.
❌ False.
Explanation: The correct distance is the diameter, which is 10 cm, not 5 cm.

Statement S: There is no point outside the circle where the tangent length is 5 cm.
❌ False.
Explanation: A tangent from an external point forms a right triangle with the radius and the line from the center to the external point. A point can exist where the tangent length = 5 cm (e.g., if the distance from the center to the external point is \(\sqrt{5^2 + 5^2} = \sqrt{50} \)). Thus, such a point exists.

Final Answer:
✅ Correct Statement: P
Distance between any pair of parallel tangents is 10 cm.