If BC, which is a chord, should have the maximum length then it should be the diameter. And since angle(BAC) is the angle subtended by the diameter at the circumference, it should be 90 degrees. And we also know that AB = AC. Hence triangle ABC is right-angles isosceles(45-45-90). Therefore, AB = AC = 10/root(2).
Hence Area = (1/2)*AB*AC
= 25 sq cm.