Question

12. In a trapezium ABCD, ABIDC which of the following is a correct statement?
(A) AO.OC = BD.OD (B) AO.OB = OC.OD (C) AB.DC = OB.OD (D) AO.OD=OC.OB
A
B​

Answer 1

Answer:

thug life Jaipal Outlook whose who's

Answer 2

ABCD is a trapezium where AB || DC and diagonals AC and BD intersect at O.

To prove

AOBO=CODO

Construction

Draw a line EF passing through O and also parallel to AB

Now, AB ll CD

By construction EF ll AB

∴ EF ll CD

Consider the ΔADC,

Where EO ll AB

According to basic proportionality theorem

AEED=AOOC ………………………………(1)

Now consider Δ ABD

where EO ll AB

According to basic proportionality theorem

AEED=BOOD ……………………………..(2)

From equation (1) and (2) we have

AOOC=BOOD

⇒ AOBO=OCOD

Hence the proof.

Therefore, AO.OB=OC.OD