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20/07/2021 4:16 pm
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Prove that the circle drawn with any side of a rhombus as diameter, passes through the point of intersection of its diagonals.
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20/07/2021 4:18 pm
To prove: A circle drawn with Q as centre, will pass through A, B and O (i.e. QA = QB = QO)
Since all sides of a rhombus are equal,
AB = DC
Now, multiply (1/2) on both sides
(1/2)AB = (1/2)DC
AQ = DP
BQ = DP
Since Q is the midpoint of AB,
AQ= BQ
Similarly,
RA = SB
Again, as PQ is drawn parallel to AD,
RA = QO
Now, as AQ = BQ and RA = QO we get,
QA = QB = QO (hence proved).