The line y = 3x - 10 intersects a circle centered at the origin at A and B. We know the lenght of chord AB is \(28\). Find the area of the circle.
+2668 Draw the line \(y=-{1 \over 3}x\).
It will intersect the original line at \((3,-1)\), and this point will also bisect the chord \(AB\)
The distance between the origin and the intersection point is \(\sqrt{10}\)
Using the Pythagorean Theorem, the radius of the circle is \(\sqrt{209}\).
Now can you find the area?
