Segments KF and KM are tangent line segments drawn to a circle of radius 4 cm.

Segments KF and KM are tangent line segments drawn to a circle of radius 4 cm. Find the lengths of the segments KM and KO if KE = 3cm.

An error was made in the problem statement. KF = 3 cm, not KE (there is no point E).

1. From point K we draw a segment to point O (the center of the circle).

2. The tangents of the circle have the same length, provided that they are drawn from the same point. Therefore, KF = KM = 3 centimeters.

3. Proceeding from the fact that the segments of tangents (according to their properties) are perpendicular to the radii at the point of tangency, we come to the conclusion that the triangles FKO and KMO are rectangular.

4. We calculate the length of the segment KO, which in the indicated triangles is the leg:

KO = √FK² + FО² (by the Pythagorean theorem) ..

KO = √3² + 4² = √9² + 16² = √25 = 5 centimeters.

Answer: KO = 5 centimeters, KM = 3 centimeters.