Chords AB and CD of a circle, when produced, meet at the point P. If…

AB = 6.3 cm,

 BP = 4.5 cm,

and CD = 3.6 cm

Let, PD = a cm

We know,

 PB × PA = PD × PC

= PB × (PB + BA) = PD × (PD + DC)

= 4.5 × (4.5 + 6.3) = a × (a + 3.6)

= 4.5 × 10.8 = x² + 3.6x

= 48.6 = a² + 3.6a

= 10a² + 36a - 486 = 0

= 5a² + 18a - 243 = 0

So, by solving further ,

here a = 5.4