Multiple choice

In a circle with centre O, PT and PS are tangents drawn to it from point P. If PT = 24 cm and OT = 10 cm Quantity I: The length of PO. Quantity II: Double the length of the hypotenuse of a right angled triangle the other two sides of which are 8 cm and 15 cm respectively.

  1. Quantity II > Quantity I

  2. Quantity I ≥ Quantity II

  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

Tangents from an external point to a circle are equal. So PT = PS = 24 cm. In right triangle OTP, PT is tangent and OT is radius. By Pythagoras: PO² = PT² + OT² = 24² + 10² = 576 + 100 = 676, so PO = 26 cm. This is Quantity I. For Quantity II: In a right triangle with sides 8 cm and 15 cm, hypotenuse = √(8² + 15²) = √(64 + 225) = √289 = 17 cm. Doubling this gives 34 cm. Since 34 > 26, Quantity II > Quantity I.

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