1
(a) Given ? ABC , construct equilateral triangles ? BCD , ? CAE, and ? ABF outside of ? ABC . Prove that AD = BE=CF .
(b)Let ABCD be a convex quadrilateral. Show that the sum of thetwo diagonals of ABCD is less than the perimeter P of ABCD, butmore than the semiperimeter P 2 of ABCD.
