ABCD is a trapezium in which in which AB is parallel to DC and it's diagram interest each other at the point O, ST AO/BO=CO/DO
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Step-by-step explanation:
construction-
draw a line OE which is||to AB and DC
in∆ABD
AB||OE so
AE/ED=BO/OD. eq. 1
and also in∆ACD
DC|| OE so
AE/ED=AO/OC. eq. 2
from eq1 and eq 2, we have
=> BO/OD=AO/CO
=> AO×OD=BO×CO
=>AO/BO=CO /OD
=>AO/BO=CO/DO. (proved)
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