# Angle of Intersection of Two circles Formula

Here you will learn what is the formula for the angle of intersection of two circles.

Let’s begin –

## Angle of Intersection of Two Circles Formula

The angle between the tangents of two circles at the point of intersection of the two circles is called angle of intersection of two circles.

If two circles are $$S_1$$ = $${x}^2 + {y}^2 + 2{g_1}x + 2{f_1}y + {c_1}$$ = 0 and $$S_2$$ = $${x}^2 + {y}^2 + 2{g_2}x + 2{f_2}y + {c_2}$$ = 0 and $$\theta$$ is the acute angle between them

then cos$$\theta$$ = |$$2{g_1}{g_2} + 2{f_1}{f_2} – {c_1} – {c_2}\over {2\sqrt{{g_1}^2 + {f_1}^2 -c_1}}{\sqrt{{g_1}^2 + {f_1}^2 -c_1}}$$|

or cos$$\theta$$ = |$${r_1}^2 + {r_2}^2 – d^2\over {2r_1 r_2}$$|

Here $$r_1$$ and $$r_2$$ are the radii of the circles and d is the distance between their centres.

Note : If the angle of intersection of two circles is a right angle then such circles are called “Orthogonal Circles“.