Question

Two chords AB and CD of a circle intersect each other at P outside the circle. If AB = 5 cm, BP = 3 cm and PD = 2cm, find CD

Answer 1

$\because$Two chords AB and CD of a circle intersect each other at P

$\therefore$ PA. PB = PC. PD [ When two chords intersect each other]

$\Rightarrow$ (AB + PB).PB = (PD + PC) PD

$\Rightarrow$(5 + 3)3 = (2 + x)(2)

$\Rightarrow$24 = (2 + x)(2)

$\Rightarrow$2 + x = 12

$\Rightarrow$x = 10