# Angle N is equal to angle A, BC = 12 CM = 6 CN = 4, find AC

March 27, 2021 | education

| You are given a triangle ABC, intersected by the secant MN, which is parallel to the base AB of the triangle.

Let’s write a short statement of the condition:

triangle ABC;

angle CNM = angle A;

BC = 12 cm;

CM = 6 cm;

CN = 4cm.

Find the side length AC -?

Decision:

So, triangles CMN and ACB are similar triangles, since angle C is the common angle, angle A = angle N (with two parallel and secant).

Triangles are similar in two corners.

From here we write down the ratio of the parties:

BC / CN = AC / CM, therefore:

AC = CM / CN * BC = (6 * 12) / 4 = 18 cm.

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