In a circle with center O, chords AB and CD intersect each other at point P. Given: PA = 2 cm, PB = 10 cm, and PC = 5 cm Find: The length of PD.

Q.In a circle with center O, chords AB and CD intersect each other at point P. Given: PA = 2 cm, PB = 10 cm, and PC = 5 cm Find: The length of PD. (a) 6 cm (b) 8 cm (c) 3 cm (d) 4 cm

Answer: D

In triangles PAD and PCB: \(\angle\)PAD = \(\angle\)PCB [both are angles subtended by arc BD] \(\angle\)PDA = \(\angle\)PBC [both are angles subtended by arc AC] ∴ Triangles PAD and PCB are similar. ∴ \(\cfrac{PA}{PC} = \cfrac{PD}{PB}\) i.e., \(\cfrac{2}{5} = \cfrac{PD}{10}\) ⇒ \(PD = 4\) ∴ DC = 5 cm.