Question

In the given figure, chords AB and CD intersect at a point P. If CP = 6, CD = 9 and AB = 19, what are the lengths of AP and PB?

Answer 1

CP = 6,  DP = CD − CP = 9 − 6 = 3 

Let AP = x, then PB = AB − AP = 19 − x 

Now  AP . PB = CP . DP 

∴ x (19 − x) = 6 × 3  ⇒ 19 x − x² = 18 

⇒ x² − 19x + 18 = 0 

⇒ (x − 1) (x − 18) = 0 

⇒ x = 1, 18 

Hence, the lengths of AP and PB are 1 unit and 18 units.