(a)[2]
State the value of $x$. Include a geometrical reason for your result.
(b)[1]
Give a geometrical reason to show that triangle $SVR$ is isosceles.
Mathematics 0580 · IGCSE · Circle theorems II
Circle theorems II — practice question
On the circle, $P$, $Q$ and $R$ lie on the circumference. $ST$ is tangent to the circle at $R$, and a second tangent from $S$ meets the circle at $V$. The diagram marks angles of $55^{\circ}$ at $P$, $65^{\circ}$ at $Q$, $60^{\circ}$ at $R$, together with $x^{\circ}$ between $QR$ and the tangent.