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The diagonals of quadrilateral A B C D...

The diagonals of quadrilateral `A B C D ,AC and B D` intersect in `Odot` Prove that if `B O=O D ,` the triangles `A B C and A D C` are equal in area.

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In `ABD`
`OB = OD`
`O` is the midpoint of `BD`
`AD` is the median
`ar(ZAOB) = ar(ZAOD) – (1)`In`/_\ CBD`
`OB = OD`
`O` is the midpoint, `OC` is the median
`ar(/_\COB) = ar(/_\COD) - (2)`
`ar(/_\AOB) + ar(/_\COB)`
`= ar(/_\AOD) + ar(/_\COD)`
Hence proved.
`ar( /_\ABC) = ar(/_\ ACD)`.
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