1972 AHSME Problems/Problem 25
Inscribed in a circle is a quadrilateral having sides of lengths , and taken consecutively. The diameter of this circle has length
We note that and so our answer is .
Let's call , , , . Let's call and . By LoC we get the relations
If we do a bit of computation we get , and . This means that .
We know that so substituting back in we get . We can clearly see that the only solution of this is or . This then means that and . If a triangle is a right triangle and is inscribed in a circle then the diameter is the hypotenuse.
This means that the diameter is so our answer is .
-Bole (edited for easier readability)