O-LevelMathematicsGeometry4024/12 · May/June 2016 · Q193 Marks
AB is a diameter of the circle, centre O. PA and QB are tangents to the circle at A and B respectively. Prove that triangle PAO is congruent to triangle QBO. Give a reason for each statement you make.
- (a)AB is a diameter of the circle, centre O. PA and QB are tangents to the circle at A and B respectively. Prove that triangle PAO is congruent to triangle QBO. Give a reason for each statement you make.[3]
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Mark scheme
Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.
- [3*] ∠POA = ∠QOB vertically opposite AO = OB equal radii ∠PAO = ∠QBO = 90° tangent perpendicular to radius
- B1 for two pairs of equal angles: ∠POA = ∠QOB and ∠PAO = ∠QBO
- or for one pair of angles and pair of sides: ∠POA = ∠QOB or ∠PAO = ∠QBO and AO = OB
- AND B1 for a correct reason linked with a correct pair of angles/sides
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