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July 22nd, 2008, 04:33 PM   #1
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Line tangent to a circle.

The line 3x + 4y - 14 = 0 is tangent to the circle with center C ( -1, -2 ). How would you determine the radius of the circle algebraically? And write the equation of the circle?
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July 23rd, 2008, 01:13 AM   #2
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Re: Line tangent to a circle.

The radius of the circle is equal to the distance from the center (-1, -2) to the line 3x + 4y - 14 = 0.

The distance from $\displaystyle (x_0 , y_0)$ to line $\displaystyle Ax + By + C = 0$ can be found by the formula:

$\displaystyle D = \frac{|Ax_0 + By_0 + C|}{\sqrt{A^2 + B^2}}$

Last edited by skipjack; February 28th, 2018 at 12:53 PM.
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