Circle cuts Circle - 1
Geometry
Level
3
Two circles of equal unit radii are orthogonal to each other. Find the length of the common chord of these two circles.
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1 solution
The equations of these two circles will be:
x^2 + y^2 = 1 .......................... (1)
(x-sqrt(2))^2 + y^2 = 1 .............(2)
Solving these two equations for x and y we see that the two circles intersect a points (0.707106,0.707106) and (0.707106, -0.707106)
Therefore the length of the common chord of these two circles is 2*0.707106 = sqrt(2)