Question

In the adjoining figure, O is the centre of a circle. Chords AB and CD intersect at P. If AB = 16 cm, CP = 6 cm, PD = 8 cm and AP $>$ PB. Then, AP is–

• A. 12 cm
• B. 24 cm
• C. 8 cm
• D. 6 cm

Answer 1

The correct option is A

12 cm

$AP\times PB=CP\times PD$

$x\times (16–x)=6times8$

$x^2-16x+48=0$

(x – 12) (x – 4) = 0. So, x = 12 or x = 4.

But AP $>$ PB. So, AP = 12 cm.