Question
Mathematics Question on Circle
The angle of intersection of the two circles x2+y2−2x−2y=0 and x2+y2=4, is
A
30∘
B
60∘
C
90∘
D
45∘
Answer
45∘
Explanation
Solution
Here circles are
x2+y2−2x−2y=0 ...(1)
x2+y2=4 ...(2)
Now, C1(1,1),r1=12+12=2
C2(0,0),r2=2
If θ is the angle of intersection then
cosθ=2r1r2r12+r22−(c1c2)2
=22.2.2+4−(2)2=21
⇒θ=45∘