Multiple choice

AB is tangent to a circle, with center O and radius 8cm, at point M. If OA = 17 cm and OB = 10 cm, then what is the length of AB? AB एक वृत्त की स्पर्शरेखा है जिसका केंद्र O ,और त्रिज्या 8cm है को बिंदु M पर स्पर्श करता है । यदि OA = 17 सेमी और OB = 10 सेमी, तो AB की लंबाई क्या है?

  1. 25 cm/सेमी.

  2. 27 cm/सेमी.

  3. 21 cm/सेमी.

  4. 17 cm/सेमी.

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C Correct answer
Explanation

Since OM is perpendicular to tangent AB at M, triangles OMA and OMB are right triangles. Using Pythagoras: AM = √(OA² - OM²) = √(289 - 64) = 15, BM = √(OB² - OM²) = √(100 - 64) = 6. So AB = 15 + 6 = 21 cm (assuming A and B are on opposite sides of M).