Question

In fig., chords AB and CD of a circle intersect at P. AP = 5cm, BP= 3cm and CP = 2.5cm. Determine the length of DP.

Answer 1

Let DP = x cm 

In Δ APC and Δ DPB 

∠ PAC = ∠ PDB  (angles in the some segment) 

∠ APC = ∠ DPB  (vertically opposite angle) 

∴ Δ APC ~ Δ DPB   {AA corollary) 

`"AP"/"DP" = "PC"/"PB"`  (similar sides of similar triangles)

`5/"x" = 2.5/3`

`=> "x" = 15/2.5 = 150/25` = 6 cm