O-LevelMathematicsGeometry4024/21 · Oct/Nov 2019 · Q77 Marks
P, Q, R and S are points on a circle. PXR and QXS are straight lines. [Figure 7 Diagram of circle with inscribed quadrilateral PQRS and intersecting diagonals PXR and QXS]
- (a)Show that triangle PQX is similar to triangle SRX. Give a reason for each statement you make.[3]
- (b)(i)PX = 8.1 cm, QX = 6.3 cm and SX = 4.5 cm. Calculate RX.[2]
- (b)(ii)Find the ratio area of triangle PQX : area of triangle PSX. Give your answer in its simplest form.[2]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- [3] ∠PXQ = ∠SXR, vertically opposite B1 for two correct pairs of angles identified ∠QPX= ∠RSX, angles in same B1 for correct reasons for two pairs of angles segment ∠PQX= ∠SRX, angles in same segment Hence similar
- [2] 3.5 M1 for RX/4.5 = 6.3/8.1 oe
- [2] 7:5 nfww B1 for 6.3 : 4.5 oe nfww
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