Points $A$, $B$ and $C$ lie on the circle with centre $O$. The line $DE$ is tangent to the circle at $C$. $AC=10$ cm, $AB=9.5$ cm and $BC=7.7$ cm.
(a)[4]
Show that angle $ABC$ is $70.2^\circ$, correct to 1 decimal place.
(b(i))[1]
Find the angle $AOC$.
(b(ii))[1]
Find the angle $ACO$.
(b(iii))[1]
Find the angle $ACD$.
(c)[3]
Calculate the radius of the circle, $OC$.
(d)[4]
Calculate the area of triangle $ABC$ and give it as a percentage of the area of the circle.
Worked solution & mark scheme
This 14-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Working: $\cos B=\dfrac{9.5^{2}+7.7^{2}-10^{2}}{2\times9.5\times7.7}$” …