Question

In the adjoining figure, chords AB and CD intersect at P. If AB = 16

cm, PD = 8 cm, PC = 6 and AP > PB, then AP = …………

(A) 8 cm (B) 4 cm

(C) 12 cm (D) 6 cm

Answer 1

Answer:

C

Step-by-step explanation:

Let the length of PA be 'x'.

Now, from properties of chords of circle we know that

PA*PB = PC*PD----(*)( This applies  if the point of intersection of chords is either inside or outside).

Given AB =16,

PB = 16-x

Given AP > PB=>x > 16 - x

=>x>8

Now Using (*) we get

x(16-x) =6*8=48

On solving for x we get x = 4 or 12 but x cannot be 4 since it should be greater than 8

Hence x=PA = 12 cm.