A bisector EF is drawn in a right-angled triangle DCE with a right angle C, with FC
| July 13, 2021 | education
A bisector EF is drawn in a right-angled triangle DCE with a right angle C, with FC = 13 cm.Find the distance from point F to line DE
The desired distance is a perpendicular drawn from point F to the hypotenuse DE.
Consider right-angled triangles ECF and EHF, in which the hypotenuse EF is common, and the angle CEF = HEF since EF is the bisector of the angle CЕD.
Then the triangle ECF is equal to the triangle EHF in hypotenuse and acute angle, and therefore FH = FC = 13 cm.
Answer: From point F to line DE 1 cm.
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