Multiple choice

(\text{Find the correct relationship between given quantities.}\\text{In a circle with centre O, PT and PS are tangents drawn to it from point P. If PT = 48 cm and OT = 20 cm}\\text{Quantity I: The length of PO.}\\text{Quantity II: Double the length of the hypotenuse of a right angled triangle the other two sides of which are 16 cm and 30 cm respectively.})

  1. Quantity II > Quantity I

  2. Quantity II ≥ Quantity I

  3. Quantity I > Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relationship cannot be established
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A Correct answer
Explanation

Quantity I: PT is tangent to circle with center O, OT is radius = 20 cm. PT ⊥ OT (tangent ⊥ radius). Triangle OTP is right-angled at T. PO² = PT² + OT² = 48² + 20² = 2304 + 400 = 2704 → PO = 52 cm. Quantity II: Right triangle with sides 16 cm and 30 cm. Hypotenuse = √(16² + 30²) = √(256 + 900) = √1156 = 34 cm. Double the hypotenuse = 2 × 34 = 68 cm. Since 68 > 52, Quantity II > Quantity I.

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