In triangle DCE, angle C = 90 degrees, bisectrix EF is drawn, FC = 13cm Find the distance from point F to line DE.

Let us prove that triangles СFE and HFE are equal.

Both triangles are rectangular, angle C, by the condition of a straight line, angle H, since FH is perpendicular to the DE side.

The hypotenuses FE are common in triangles, and the angle HEF = CEF, since the segment EF is the bisector of the DEC angle.

Then triangles CFE and HFE are equal in the third sign of equality of right-angled triangles, in hypotenuse and acute angle.

Then the segment FH = CF = 13 cm.

Answer: The distance from point F to line DE is 13 cm.