SOLUTION: Find the equation of the SMALLEST circle tangent to the line {{{ x+sqrt( 3 )y-2sqrt( 3 ) = 0 }}} and the coordinate axes. Please help me solve this problem. Best regards!

Question 942828: Find the equation of the SMALLEST circle tangent to the line

and the coordinate axes.
Please help me solve this problem. Best regards!
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Smallest? There's only one solution.
Use the x and y intercepts.
They form a right triangle with a circle inscribed in that right triangle.
x-intercept :

y-intercept :

So you have a right triangle triangle with one leg, , and another leg, .
Find the hypotenuse using the Pythagorean theorem,

For an inscribed circle in a right triangle,

So the equation of the circle is,

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