The Total solution for NCERT class 6-12
Prove that the circle drawn with any side of a rhombus as diameter,passes through the point of intersection of its diagonals.
To prove: A circle drawn with Qas centre, will pass through A, B and O (i.e. QA = QB = QO)
Since all sides of arhombus are equal,
AB = DC
Now, multiply (½) onboth sides
(½)AB = (½)DC
So, AQ = DP
BQ = DP
Since Q is themidpoint of AB,
AQ= BQ
Similarly,
RA = SB
Again, as PQ is drawnparallel to AD,
RA = QO
Now, as AQ = BQ and RA= QO we get,