The line y = 3x - 10 intersects a circle centered at the origin at A and B. We know the lenght of chord AB is \(18\). Find the area of the circle.
+2668 Draw a line segment connecting the points \((0,0)\) and \((3,-1)\). This segment is perpendicular to the line \(y = 3x-10\).
The distance between the two points is \(\sqrt {10}\).
Note that the point \((3,-1)\) bisects chord AB.
We know have a right triangle with legs \(\sqrt{10}\), 9, and a hypotenuse r.
Using the Pythagorean Theorem, we find that \(r = \sqrt{91}\)
The formula for the area of a circle is \(\pi r^2\).
You can take it from here, I suppose?
