O is the center of the circle. Its two chords AB and CD intersect each other at the point P (internally) within the circle. If AB = 22 cm, PB = 14 cm, and CP = 8 cm, then find the value of the PD.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 14 cm.
From the given question the figure can be drawn as follows
Now,
If two chords AB and CD intersect each other at point P inside the circle, then
AP × PB = CP × PD
So,
⇒ (AB - PB) × PB = CP × PD
⇒ (22 - 14) × 14 = 8 × PD
⇒ 8 × 14 = 8 × PD
⇒ PD = 14 cm