Problem: A circle passes through the vertices of a triangle with side-lengths 721​, 10,1221​. The radius of the circle is:
Answer Choices:
A. 415​
B. 5
C. 425​
D. 435​
E. 2152​​
Solution:
Method I. Since (721​)2+102=(1221​)2, the triangle is right with hypotenuse 1221​. Therefore, D=2R=1221​,R=25/4.
Method II. R=4 Kabc​=4 s( s−a)(s−b)(s−c)​abc​=415(221​)(5)(721​)​(1221​)(10)(721​)​=425​.