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.

Guest Apr 26, 2022

#1**+1 **

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?

BuilderBoi Apr 26, 2022