Central Angles , Circles, Inscribed Angles

Question

Rex assigned distinct points A, B, C, and D on a circle with diameter 25. He connects the consecutive points constructing quadrilateral ABCD. If angle A is equal to 90 degrees, and all sides are distinct integers, what is the perimeter of quadrilateral ABCD?

Answer 1

Not sure it's possible to get integer sides with a diameter = 25 and one angle =90 degrees, but

a rectangle with vertices (6,11), (-6,11), (-6,-11) and (6,11) comes close although the y coordinates are very slightly less than 11 or slightly more than -11.

Then perimeter = 4(11+6) = 4(17) = 68