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 =

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 =

Philoid · Accepted Answer

Given: AB = 16 cm, PD = 8 cm, and PC = 6 cm

We know that two chords AB and CD intersect at P inside the circle with centre at O.

Then PA× PB = PC× PD.

Let PA = x then PB = AB – AP = 16 – x

⇒ x × (16–x) = 6× 8

⇒ 16x – x² =48

⇒ x² – (12+4)x + 48 = 0

⇒ (x–12)(x –4) =0

⇒ x = 4 and 12

x = 4 is not possible because AP >PB

⇒ AP = 12 cm