1MA0 Higher June 2016 Paper 1 Q20
*20
Diagram NOT accurately drawn
\(P\), \(M\) and \(S\) are points on a circle, centre \(O\).
\(RST\) is a tangent to the circle.
Angle \(PSO = 48^\circ\)
\(MP = MS\)
Work out the size of angle \(MST\).
Give reasons for each stage of your working. (5)
| Answer | Mark | Notes |
|---|---|---|
| \(69^\circ\) (supported) | 5 | M1 for method to find angle \(PSR\) eg \(90 - 48\) (= 42) or method in triangle \(POS\) to find angle \(POS\) (= 84) M1 for method to find angle \(PMS\) (= 42) A1 cao C2 (dep on at least M1) for correct and complete set of appropriate reasons (C1 for one correct reason involving a circle theorem supported by working) eg The tangent to a circle is perpendicular (90) to the radius (diameter) Alternate segment theorem. Angles in a triangle add up to 180 Base angles of an isosceles triangle are equal. The angle at the centre of a circle is twice the angle at the circumference. |