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.