Multiple choice

There are two chords AB and DC of a circle C (O, r). Chord AB and DC, interest each other at P when produced. If AB = 13 cm. CD=9 cm., PC=6 cm. then find the value of BP. एक वृत्त C (O, r) में दो जीवाएँ AB और DC हैं। जीवा AB और DC एक दूसरे को P पर बढ़ाने पर मिलती हैं। यदि AB =13 सेमी. , CD=9 सेमी. PC=6 सेमी. तो BP का मान ज्ञात कीजिए।

  1. 4 cm./सेमी

  2. 5 cm./सेमी

  3. 6 cm./सेमी

  4. 8 cm./सेमी
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B Correct answer
Explanation

For two intersecting chords, the products of the segments are equal: AP × BP = CP × DP. Given AB = 13, so AP = 13 - BP. Also CD = 9 and PC = 6, so PD = 9 - 6 = 3. Then (13 - BP) × BP = 6 × 3 = 18. Solving BP² - 13BP + 18 = 0 gives BP = 4 or 9. Since AB = 13 and BP must be less than AB, BP = 4 cm.

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