2026 YTSS P2 Q3

\(A,B,C,D\) and \(F\) are points on a circle in the diagram above. \(O\) is the centre of the circle.

Line \(AE\) meets line \(OC\) at \(O\).

The line \(AF\) cuts the line \(DC\) at \(P\).

The ratio of angle \(AOC\) to angle \(ABC\) is \(4:3\).

1. Show that the angle \(AFC\) is \(72^\circ\). Give a reason for each step of your working.[2]
2. Find the perimeter of the major sector \(ADFC\), given that the diameter of the circle with centre \(O\) is 11 cm.[2]
3. Another circle is drawn on the diagram such that line \(AD\) is its diameter.
   Determine whether point \(E\) lies on its circumference if \(\angle DAO=18^\circ\). Give reasons for each statement you make.[2]