Answer:
FK = BE .... Proved.
Explanation:
See the given diagram with all the details.
Now, if we consider Δ BFK and Δ BDE, then
(i) BF = BD {Given}
(ii) ∠ BFK = ∠ BDE = 90° {Since FK ⊥ AB and DE ⊥ AC also given}
and (iii) ∠ B is the common angle.
Therefore, by Angle-Side-Angle i.e. ASA criteria we can say Δ BFK ≅ Δ BDE.
Therefore, FK = BE {Corresponding sides of congruent triangles }
(Proved)