On the circle centred at $O$, the points $A$, $B$, $C$ and $D$ are all located on the circumference. The given angles are $\angle ADC = 128^\circ$, $\angle ACD = 28^\circ$ and $\angle BCO = 30^\circ$. NOT TO SCALE.
(a(i))[3]
Show that the angle $AOC$ is obtuse and equals $104^\circ$. Give a reason for every step in your working.
(a(ii))[2]
Find the value of angle $BAO$.
(a(iii))[1]
Find the value of angle $ABD$.
(a(iv))[3]
Calculate the complete perimeter of sector $OADC$.
(b(i))[3]
Calculate the cross-sectional area of the larger prism.
(b(ii))[3]
Calculate the sphere's radius.
Worked solution & mark scheme
This 15-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Angles opposite each other in a cyclic quadrilateral” …