1MA0 Higher March 2013 Paper 1 Q19

EdexcelHigherOld spec3 marksCircle Theorems

Circle centre O with diameter BOD and point A on the circle; BC and AC are tangents meeting at C, angle OCB = 34 degrees

Diagram NOT accurately drawn

\(A\), \(B\) and \(D\) are points on the circumference of a circle, centre \(O\).
\(BOD\) is a diameter of the circle.
\(BC\) and \(AC\) are tangents to the circle.
Angle \(OCB = 34^\circ\).

Work out the size of angle \(DOA\). (3)

Mark scheme

Answer	Mark	Notes
68	3	M1 for angle \(OBC = 90^\circ\) or angle \(OAC = 90^\circ\) (may be marked on the diagram or used in subsequent working) M1 for correct method to find angle \(BOC\) or \(AOC\) or \(AOB\) e.g. angle \(BOC = 180 - 90 - 34\) (\(= 56\)) or angle \(AOC = 180 - 90 - 34\) (\(= 56\)) or angle \(AOB = 180 - 2 \times 34\) (\(= 112\)) A1 cao NB (68 must be clearly stated as an answer and not just seen on diagram)