In triangle ABC, bisector BD is perpendicular to side AC. The bisector AF is 24 cm. Find the length of the bisector CE.

Since the bisector BD is perpendicular to the AC side, it is the height. Then triangle ABC is isosceles (by the property of an isosceles triangle), the side AB is equal to the side BC, and the bisector AF is equal to the bisector CE.
Answer: the required length of the bisector CE is 24.



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