Number three was a little technical so I thought maybe I'd toss out a hint. Construct lines AP, BP and CP. These three lines, together with line segments a, b and c, divide the equilateral triangle into six smaller triangles. Calculating the area of them, and doing a lot of algebra, should get you where you need to go.
That worked for me! Thanks for the advice!
For number three, couldn't you just extend line segment DE to an infinite line and then use BF 5 to prove that angle A = angle D and angle B = angle E?
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