1MA0 Higher November 2014 Paper 2 Q17

EdexcelHigherOld spec4 marksCircle Theorems

Circle centre O with diameter AC; chord BD crosses AC at E; angle CAB is 25 degrees and angle DEC is 100 degrees

Diagram NOT accurately drawn

\(A\), \(B\), \(C\) and \(D\) are points on the circumference of a circle, centre \(O\).
\(AC\) is a diameter of the circle.
\(AC\) and \(BD\) intersect at \(E\).

Angle \(CAB = 25^\circ\)
Angle \(DEC = 100^\circ\)

Work out the size of angle \(DAC\).

You must show all your working. (4)

Mark scheme

Answer	Mark	Notes
\(35^\circ\)	4	M1 for \(ABC = 90\) M1 for \((ACB =)\ 180 - 90 - 25\) (= 65) M1 for \((DBC =)\ 180 - \text{'}65\text{'} - 80\) (=35) A1 cao supported by working OR M1 for \((AOB =)\ 180 - 2 \times 25\) (= 130) M1 for \((ADB =)\ 130 \div 2\) (=65) M1 for \((DAC =)\ 180 - 65 - 80\) A1 cao supported by working.