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 एक वृत्त में जिसका केंद्र O हे, PT और PS में बिंदु P से स्पर्श रेखाएं हैं । यदि PT = 24 सेमी और OT = 10 सेमी 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. Quantity I: PO की लम्बाई Quantity II: एक समकोण त्रिभुज के कर्ण की लंबाई का दो गुना जिसकी भुजाएं क्रमशः 8 सेमी और 15 सेमी हैं ।

  1. Quantity II > Quantity I मात्रा II > मात्रा I

  2. Quantity I ≥ Quantity II मात्रा I ≥ मात्रा II

  3. Quantity I > Quantity II मात्रा I > मात्रा II

  4. Quantity I ≤ Quantity II मात्रा I ≤ मात्रा II

  5. Quantity I = Quantity II or relationship cannot be established मात्रा I = मात्रा II या संबंध स्थापित नहीं किया जा सकता
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A Correct answer
Explanation

Quantity I: PT is tangent to circle with center O, so OT is perpendicular to PT. Triangle PTO is right-angled at T. PO = √(PT² + OT²) = √(24² + 10²) = √(576 + 100) = √676 = 26 cm. Quantity II: Right triangle with sides 8 cm and 15 cm. Hypotenuse = √(8² + 15²) = √(64 + 225) = √289 = 17 cm. Double the hypotenuse = 2 × 17 = 34 cm. Comparing: Quantity II (34 cm) > Quantity I (26 cm).

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