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

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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