Review question

# Can we show that (circle area)/(triangle area) $\geq \pi$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7656

## Question

Let $p$ and $q$ be positive real numbers. Let $P$ denote the point $(p,0)$ and $Q$ denote the point $(0,q)$.

1. Show that the equation of the circle $C$ which passes through $P$, $Q$ and the origin $O$ is $x^2 - px + y^2 - qy = 0.$ Find the centre and area of $C$.

2. Show that $\frac{\text{area of circle C}}{\text{area of triangle OPQ}} \ge \pi.$

3. Find the angles $OPQ$ and $OQP$ if $\frac{\text{area of circle C}}{\text{area of triangle OPQ}} = 2\pi.$