Angle of Intersection of Two Circles

Q.

The angle at which the circles $(x-1{)}^2+y^2=10and{x}^2+(y-2{)}^2=5$ intersect is

1. $\frac{\pi }{6}$

2. $\frac{\pi }{4}$

3. $\frac{\pi }{3}$

4. $\frac{\pi }{2}$

Q.

If $d_1,d_2,d_3$ are the diameters of the three ascribed circles of a triangle, then $d_1{d}_2+d_2{d}_3+d_3{d}_1$ is equal to

1. $4s^2$

2. ${△}^2$

3. $4{△}^2$

4. $2{△}^2$

Q. If a$\ne$b then the length of common chord of the circles ${\left(x-a\right)}^2+{\left(y-b\right)}^2=c^2$ and ${\left(x-b^{}\right)}^2+{\left(y-a\right)}^2=c^2$ is

1. $\sqrt{3c^2-{\left(a-b\right)}^2}$
2. $\sqrt{2c^2-{\left(a-b\right)}^2}$
3. $\sqrt{c^2-{\left(a-b\right)}^2}$
4. $\sqrt{4c^2-2{\left(a-b\right)}^2}$