Review question

# When will the arclength $QR$ take a maximum value? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8936

## Question

$P$ is a point on the circumference of a circle $X$ of diameter $\quantity{3}{in.}$ An arc of another circle $Y$ is drawn with centre $P$, intersecting $X$ at $Q$ and $R$. Express the lengths of $PQ$ and the minor arc $QR$ of $Y$ in terms of $\theta$, where $\theta$ is the angle, in radians, between $PQ$ and the diameter of $X$ through $P$.

Prove that the length of the arc $QR$ has a stationary value when $\theta = \cot \theta$, and that this value is a maximum.