1MA0 Higher November 2013 Paper 1 Q22
*22
Diagram NOT accurately drawn
\(A\), \(B\), \(C\) and \(D\) are points on the circumference of a circle, centre \(O\).
Angle \(AOC = y\).
Find the size of angle \(ABC\) in terms of \(y\).
Give a reason for each stage of your working. (4)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(360 - y\) | \(180 - \dfrac{y}{2}\) | 4 | M1 \(ADC = \dfrac{y}{2}\) A1 \(180 - \dfrac{y}{2}\) C2 (dep on M1) for both reasons Angle at centre is twice the angle at the circumference Opposite angles in cyclic quadrilateral add to 180˚ (C1 (dep on M1) for one appropriate circle theorem reason) OR M1 reflex \(AOC = 360 - y\) A1 \(\dfrac{360 - y}{2}\) oe C2 (dep on M1) for both reasons Angles around a point add up to 360˚ Angle at centre is twice the angle at the circumference (C1 (dep on M1) for one appropriate circle theorem reason) |