Multiple choice

Chords AB and CD of a circle intersect externally at P. If AB = 6 cm, CD = 3 cm and PD = 5 cm, then the length of PB is- एक वृत्त की दो जीवा AB तथा CD एक दूसरे को वृत्त के बाहर बिन्दु P पर प्रतिच्छेदित करती है। यदि AB= 6 सेमी CD= 3 सेमी तथा PD= 5 सेमी. हो तब PB की लम्बाई ज्ञात कीजिए?

  1. 5 cm/सेमी

  2. 7.35 cm/सेमी

  3. 6 cm/सेमी

  4. 4 cm/सेमी

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For chords intersecting externally at P: PA × PB = PC × PD. With AB = 6, let PB = x, so PA = x + 6. With CD = 3 and PD = 5, PC = 5 + 3 = 8. Then (x + 6)x = 8 × 5 = 48, giving x² + 6x - 48 = 0. Factoring (x + 12)(x - 4) = 0, so x = 4 (positive length). PB = 4 cm.