Then O(h,k) lies on the diameter 3y=x+10, so that 3k=h+10. Also, OA=OB (radii of the same circle), so that
(h+6)2=(h−4)2. That is, h=−1 and therefore, k=3.
Hence radius of the circle is
OA=√(−1+6)2+(3−7)2
=√25+16=√41
so that AC, the diameter of the circle, is 2√41
.Now, AB=√(−6−4)2+(7−7)2=10
⇒BC=√164−100=8
Thus required area of the rectangle is AB×BC=10×8=80sq.units