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Question

State true or false:

In the given figure, the diagonals AC and BD intersect at point O . If OB=OD and AB//DC, then
Area(DOC)=Area(AOB).

187405_2c47fa78a66644df82cf66a5f223c81b.jpg

A
True
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B
False
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Solution

The correct option is A True
Given, the diagonals AC and BD intersect at point O such that OB=OD and ABDC.
Now, In DOC and AOB
BDC=DBA (Alternate angles, As ABCD and BD intersects it.)
OD=OB (Given)
DOC=AOB ( Vertically opposite angles)
So, DOCAOB (By ASA concurrence Property)
Since, Concurrent triangle have equal areas.
Area of DOC= Area of AOB

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