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The line \(y = \frac{3x + 15}{4}\) intersects the circle \(x^2 + y^2 = 36\) at points A and B. Find the distance between A and B.

 Jun 2, 2020
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The intersections are (12/13*(3*sqrt(3) - 1),6/13*(3 + 4*sqrt(3)) and (-12/13*(1 + 3sqrt(3)), -6/13*(4*sqrt(3) - 3), so the length of the chord is sqrt((12/13*(3*sqrt(3) - 1 + 12/13*(1 + 3*sqrt(3))^2 + (6/13*(3 + 4*sqrt(3)) + 6/13*(4*sqrt(3) - 3))^2) = 24*sqrt(39)/13.

 Jun 3, 2020

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