MHB Length of $\overline{CE}$ in Square $ABCD$ with $45^o$ Angle

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In square ABCD with side length 13, points E and F are located on sides BC and AB, respectively, forming a 45-degree angle at point D with a line segment EF measuring 11 units. The problem requires calculating the length of segment CE. Geometric relationships and trigonometric principles are utilized to derive the necessary lengths and angles. The solution involves applying the properties of right triangles and the Pythagorean theorem. Ultimately, the length of segment CE is determined through these calculations.
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A square $ABCD$ , each side with length 13,
if points $E,F$ on $\overline{BC} ,\overline{AB} $ respectively,$\angle EDF=45^o,$and $\overline{EF}=11$
find length of $\overline{CE}=?$
 
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Albert said:
A square $ABCD$ , each side with length 13,
if points $E,F$ on $\overline{BC} ,\overline{AB} $ respectively,$\angle EDF=45^o,$and $\overline{EF}=11$
find length of $\overline{CE}=?$
hint:
use pythagorean theorem
 

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