Question

Abcd is a trapezium in which ab parallel cd and it's diagonal intersect each other at the point o . Show that oa/ob=co/do

Answer 1

As, OA = OC = 1/2 AC

OB = OD = 1/2 DB

OA/OB = OC/OD

If we cross multiply, then we get

OA * OD = OB * OC

By transposing process we get,

OA /OC = OB /OD (As OA = OC and OB = OD)

i. e. 1 = 1

Hence proved.