Problem: Inscribed in a circle is a quadrilateral having sides of lengths , and taken consecutively. The diameter of this circle has length
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since angles and are supplementary, (See figure) one suapects that each may be a right angle. This turns out to be the cace with dingonal of length as the common hypothenuse and the diameter of the circumecribing circle.
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or
The ame result may be obtained using the Law of Cosines on triangles and . Thus
Since is the supplement of , replacing by its equal ( ) and subtracting, gives
and and its supplement are both right angles. The common hypothenuse has length and is the diameter of the circumscribing circle as before.