TMUA Rosie's Papers Set A Paper 1 · Question 18

A circle $C$ has a radius of $r$ and is centred at the origin $(0,0)$ . A fixed point $P$ lies outside the circle at the coordinates $(d,0)$ , where $d>r$ . Two tangent lines are drawn from $P$ to touch the circle at two points, $A$ and $B$ . A chord is then drawn connecting $A$ and $B$ , with this chord intersecting the $x$ -axis at a point $Q$ . Which of the following expressions represents the $x$ -coord of $Q$ ?

\frac{r^2}{d}

\frac{r^3}{d^2}

d-\frac{r^2}{d}

\sqrt{d^2-r^2}

\frac{rd}{\sqrt{d^2-r^2}}

examday

Rosie's Papers Set A Paper 1 · Q18