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ABC is a right-angled triangle with right angle at A, and AB > AC. Let D...

ABC is a right-angled triangle with right angle at A, and AB > AC. Let D be the midpoint of the side BC, and let L be the bisector of the right angle at A. Draw a perpendicular line to BC at D, which meets the line L at point E. Prove that

(a) AD=DE; and

(b) ∠DAE=1/2(∠C−∠B)

Hint: Draw a line from A perpendicular to BC, which meets BC in the point F

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