Question

ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that `("AO")/("BO") = ("CO")/("DO")`

Answer 1

Draw a line EF through point O, such that EF || CD

In ΔADC, EO || CD

By using basic proportionality theorem, we obtain

`("AE")/("ED") = ("AO")/("OC")`              ...(1)

In ΔABD, OE || AB

So, by using basic proportionality theorem, we obtain

`("ED")/("AE") = ("OD")/("BO")`

⇒ `("AE")/("ED") = ("BO")/("OD")`             ...(2)

From equations (1) and (2), we obtain

⇒ `("AO")/("OC") = ("BO")/("OD")`

⇒ `("AO")/("BO") = ("OC")/("OD")`