1MA0 Higher June 2017 Paper 1 Q22
*22
Diagram NOT accurately drawn
\(B\), \(C\) and \(D\) are points on the circumference of a circle, centre \(O\).
\(ABO\) is a straight line.
\(AD\) is the tangent at \(D\) to the circle.
Angle \(DAO = 40^\circ\)
Work out the size of angle \(BCD\).
Give a reason for each stage of your working. (5)
| Answer | Mark | Notes |
|---|---|---|
| \(155^\circ\) | 5 | M1 for a method to find angle \(AOD\) e.g \(90 - 40\) (= 50) M1 for a complete method to find angle \(BCD\) eg \(360 - \text{\textquoteleft}50\text{\textquoteright}\) (= 310) and \(\text{\textquoteleft}310\text{\textquoteright} \div 2\) (= 155) A1 for 155 C2 for complete reasons for their method Angle between tangent and radius = 90 Angle at the centre is twice the angle at the circumference oe Angle sum of a triangle = 180 Sum of angles round a point = 360 (C1 for at least two reasons, one of which must be a circle theorem) OR M1 for a method to find angle \(AOD\) eg \(90 - 40\) (= 50) M1 for a complete method to find angle \(BCD\) eg \(50 \div 2\) (= 25) and \(180 - \text{\textquoteleft}25\text{\textquoteright}\) (= 155) A1 for 155 C2 for complete reasons for their method Angle between tangent and radius = 90 Angle at the centre is twice the angle at the circumference oe Opposite angles of a cyclic quadrilateral add up to 180 Angle sum of a triangle = 180 (C1 for at least two reasons, one of which must be a circle theorem) |