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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 \(28\).  Find the area of the circle.

 Apr 29, 2022
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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?

 Apr 29, 2022

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