The segments AB and DC lie on parallel lines, and the segments AC and BD intersect at point M.

The segments AB and DC lie on parallel lines, and the segments AC and BD intersect at point M. Find the MC if AB = 15, DC = 30, AC = 39.

Since the angles AMB and CMD are vertical, and the segments AB and DC lie on parallel straight lines, therefore, the angles of triangles AMB and CMD are equal.

It follows from this that triangles AMB and CMD are similar.

By the property of similarity of triangles:

DC / AB = MC / AM;

Or, DC / AB = MC / (AC – MC) = MC / (39 – MC).

Substitute the known values and solve the resulting equation for the MS.

30/15 = MC / (39 – MC),

MC = 2 * (39 – MC),

3 * MC = 78,

MC = 26.