The centers of three externally tangent circles form a right angled triangle with legs units and units. What is the sum of the circumferences of the circles?
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We recognize the right triangle with sides of 6 and 8 as a scaled up version of the 3-4-5-triangle. Therefore the third side of the triangle is 1 0 units. If the radii of the circles are a , b and c , we can set up the equations
We can solve this linear system of equations to get
The circumference of a circle with radius r is given by 2 π r , so the circumferences of the three circles are
Their sum is