O-LevelMathematicsGeometry4024/12 · Oct/Nov 2020 · Q234 Marks
In the diagram, the circles with centres O and Q touch at P where OPQ is a straight line. The line ORT intersects the smaller circle at R and is a tangent to the larger circle at T. OR = 4 cm and RT = 6 cm. The radius of the larger circle is x cm. Calculate the value of x.
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 (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [4] Use of Pythagoras leading to 10.5 oe
- B1 for OP = 4 and PQ = x soi
- M1 for OQ² = OT² + TQ² oe soi
- B1 for x² + 4x + 4x + 16 seen or x² + 8x + 16 seen
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