GATE 2021 EE – Question 23
Suppose the circles $x^2+y^2=1$ and $(x-1)^2+(y-1)^2=r^2$ intersect each other orthogonally at the point $(u,v)$. Then $u+v=$ ________.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 1
Explanation
Two circles are orthogonal when the square of the distance between their centres equals the sum of the squares of their radii: $(0-1)^2+(0-1)^2=2=1+r^2$, so $r=1$. The intersection points of the two unit circles centred at $(0,0)$ and $(1,1)$ are $(1,0)$ and $(0,1)$, so $u+v=1$.