Multiple choice

In a circle with centre O and radius 6.5 cm, a chord AB is at a distance 2.5 cm from the centre. If tangents at A and B intersect at P, then find the distance of P from the centre.

  1. 16.9

  2. 18.9

  3. 15.3

  4. 17.2

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A Correct answer
Explanation

जीवा AB की लंबाई = 2√(6.5² - 2.5²) = 12 cm (पाइथागोरस प्रमेय)। समरूप त्रिभुजों OAM और PAM से, PA/AM = OA/OM = 6.5/2.5 = 13/5, अतः PA = 15.6 cm। समकोण त्रिभुज OAP में, OP² = 6.5² + 15.6² = 285.61, OP = 16.9 cm।