Points $A$, $B$, $C$ and $D$ lie on the circle with centre $O$. $TA$ and $TC$ are tangents to the circle. $T$, $D$, $O$ and $B$ are on one straight line. $\angle ATO = x^\circ$.
(a)[3]
Show that triangle $OAT$ is congruent to triangle $OCT$. Give a reason for every statement you make.
(b(i))[1]
Find, in terms of $x$, $\angle AOT$.
(b(ii))[1]
Find, in terms of $x$, $\angle OAB$.
(b(iii))[1]
Find, in terms of $x$, the reflex $\angle ADC$.
(c)[3]
The circle has radius $6\text{ cm}$. If $x = 35^\circ$, determine $BT$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Tangent is perpendicular to radius” …