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Prove that the circle drawn with any sid...

Prove that the circle drawn with any side of a rhombus as a diameter, posses through the point of intersection of its diagonals.

Text Solution

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We conclude from the given information
`ABCD` is a rhombus.
Construction
Circle is drawn taking side `CD` diameter. Lets assume the diagonals `AC` and `BD` intersect at `O`.
Proof:
`/_DOC=90^@`(Angle in the semicircle) and diagonals of rhombus bisect at right angles at`O`
`:./_DOC=/_COB=/_BOD=/_AOD=90^@`
`:.`Circle passes the point of intersection of its diagonal through `O`.
Hence proved.
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