Finding Segment Length Using Angle Bisector Theorem

In triangle ABC, angle A measures 60 degrees. The length of side AB is 14 units, and the length of side AC is 10 units. Point D lies on side BC such that AD is the angle bisector of angle A. Your task is to find the length of segment BD.

Use the angle bisector theorem, which states that the ratio of the lengths of the two segments created by the angle bisector on the opposite side is equal to the ratio of the lengths of the two other sides adjacent to the angle:

Express the length of segment BD in simplest form.