I'll just explain how to prove it. You can write up a
two-line proof of it.
Let O be the center of the circle. Draw in four radii, OA, OC, OD, OE.
Triangle AOD is congruent to triangle COE by SSS since AD and CE are
given congruent and the other sides are radii of the same circle.
Therefore angles DAO and ECO are congruent by CPCT.
Triangle AOC is isosceles because it has two sides OA and OC which are both
radii of the same circle and are congruent.
Therefore angles OAC and OCA are congruent because they are
the base angles of isosceles triangle AOC.
Angles DAC and ECA are congruent because they are, respectively,
the sums of angles DAO+OAC and ECO+OCA.
Therefore Triangle ABC is isosceles since its base angles DAC and
ECA are congruent.
Edwin
