In a rectangular DCE track with a right angle C, the bisector EF was drawn, with fc = 13cm.

In a rectangular DCE track with a right angle C, the bisector EF was drawn, with fc = 13cm. Find the distance from point F to line DE.

Let us prove that the triangle CFE is equal to the triangle HFE.

Right triangles CFE and HFE have a common hypotenuse FE.

The angle FEH of the triangle FHE and the angle FEC of the triangle FCH are equal, since by condition, ЕF is the bisector of the angle CED.

Then right-angled triangles CFE and HFE are equal in hypotenuse and acute angle.

Since the triangles are equal, then CF = HF = 13 cm.

Answer: Distance from point F to line DE = 13 cm.