Question

In quadrilateral ABCD, the diagonals AC and BD intersect each other at point O. If AO = 2CO and BO = 2DO, show that OA × OD = OB × OC.

Answer 1

Given

AO = 2CO → `(AO)/(CO) = 2` and

BO = 2DO → `(BO)/(DO) = 2`

Therefore, `(AO)/(CO) = (BO)/(DO)`

On cross-multiplication,

AO × DO = BO × CO

That is,

OA × OD = OB × OC

Hence proved.