# A mouse on a ring

Calculus Level 4

A mouse is running along a circle of radius 1, with center $$(1,0)$$ at a constant speed 1. A lazor is positioned at the origin, and pointed towards the mouse at all times. The mouse started running at the origin, at time $$t=0$$.

Given that the angle the lazor makes with the horizontal (the blue line in the GIF) at time $$t$$ is $$f(t)$$, and that

$\int _{ 0 }^{ \pi }{ f(t) } \ dt=\frac { A{ \pi }^{ B } }{ C }$

Find the value of $$A+B+C$$

$$\bullet$$ $$f(t)$$ is in radians.

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