Circumcentre এর লীলাখেলা

[shehab ahmed]

Let ABCD be a quadrilateral.AC and BD intersect at P.Let the circumcentres of ADP and BPC are Q and R respectively.Let the midpoints of AC,BD and QR are M,N,O respectively.Prove that the circumcentre of MNP is O

[shehab ahmed]

Hint

if one vertex of a triangle is $0$ and the other two vertices are $x$ and $y$ then the circumcentre of that triangle is given by
$\frac {xy(x'-y')}{x'y-xy'}$ where $a'$ is the conjugate of $a$