Through point M outside the circle tangents MA and MB are drawn, and through point C on the circle

Through point M outside the circle tangents MA and MB are drawn, and through point C on the circle a tangent is drawn, intersecting the segments MA and MB at points K and L. Prove that the perimeter of triangle KML does not depend on the position of point C.?

The perimeter of the KML triangle is: Rkml = MK + ML + KL.

KL = KС + LС, then Rkml = (KM + KС) + (ML + LS).

By the property of tangents drawn from one point, KС = KА, LВ = ЛС, then:

Rkml = (KM + KA) + (ML + LВ) = MA + MВ.

Thus, the perimeter of the triangle is equal to the sum of dyn tangents MA and MB and does not depend on the position of point C, which was required to prove.