Question

construct an rhombus inscribing a circle​

Answer 1

The diagonals of a rhombus are perpendicular, so ABO is a right triangle with right angle at the center O. The legs are 6 and 10, so the hypotenuse AB has length sqrt(136). The radius you seek is the perpendicular OP from O to AB. Suppose that.|OP| = x and use similar triangles to get x:10 = 6:sqrt(136). x is 30/sqrt(34), which is about 5.145.