Problem: If r is positive and the line whose equation is x+y=r is tangent to the circle whose equation is x2+y2=r, then r equals
Answer Choices:
A. 21
B. 1
C. 2
D. 2
E. 22
Solution:
If the line equation x+y=r is tangent to the circle equation x2+y2=r then the distance between the point of tangency (2r,2r) and the origin is r. Therefore, (2r)2+(2r)2=r and r=2.