In the given figure, P is outside the circle and secants PCA and PDB intersect the circle at C and A, D and B respectively.

Question

In the given figure, P is outside the circle and secants PCA, and PDB intersects the circle at C and A, D, and B respectively. If PA = 24, CA = 16 and DB = 26, find PB.

Answer 1

Let PD = x 

PD × PB = PC × PA 

⇒ x (x + 26) = 8 × 24 

⇒ x² + 26x − 192 = 0 

⇒ (x + 32) (x − 6) = 0 

⇒ x = 6, taking only positive value of x. 

⇒ PB = 6 + 26 = 32.