Construct P by the recipe KP = (KM)*(KN)*(KO) (as complex numbers). Then take Q on OP such that QP/QO = n remains constant.

The locus of Q as M moves on the circle c is curve k.

Switch to the "Select on contour" tool (Ctrl+2) and pick-move point O (changing the ratio m). The ratio OK/OP remains fixed, the curve k transforms to a similar one.

Pick-move point Q on OP (changing the ratio n). The curve k changes its shape. However the curve (modulo similarity) does not depend on the measure of angle <(JIH). Though it depends on the radius of the circle c.

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