Problem: A circle is inscribed in a triangle with sides 8,158,158,15, and 171717. The radius of the circle is:
Answer Choices:
A. 666
B. 222
C. 555
D. 333
E. 777 Solution:
This is a right triangle. For any right triangle it can be shown (see 1950, Problem 35) that
a−r+b−r=c.∴2r=a+b−c=8+15−17=6a-r+b-r=c . \quad \therefore 2 r=a+b-c=8+15-17=6 a−r+b−r=c.∴2r=a+b−c=8+15−17=6
and r=3r=3r=3.