O-LevelMathematicsGeometry4024/12 · May/June 2017 · Q174 Marks
In the diagram, P, Q, R, S and T lie on the circle. QT is a diameter of the circle, centre O. X is the point of intersection of PS and QT. P\hat{X}T = 125° and P\hat{S}Q = 35°. [Figure: Circle with points P, Q, R, S, T. QT is diameter through O. PS intersects QT at X. Angles PXT=125°, PSQ=35° are marked.]
- (a)Complete the following statement with a geometrical reason. P\hat{T}Q = 35° because ................................................................................................................[1]
- (b)Find P\hat{O}T.[1]
- (c)Find S\hat{P}Q.[1]
- (d)Find S\hat{R}Q.[1]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [1] (a) Angles in same segment are equal
- [1] (b) \angle PQT = 55°
- [1] (c) \angle SPQ = 70°
- [1] (d) \angle SRQ = 110°
- FT 180 - their (c)
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