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.