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# coordinates

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127
1

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

#1
+2541
0

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