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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.

 Apr 26, 2022
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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?

 

 Apr 26, 2022

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