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# Coordinates

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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

### 1+0 Answers

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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