O-LevelMathematicsGeometry4024/12 · May/June 2019 · Q245 Marks

[Figure of circle with points A, B, C, O, P, Q] A, B and C are points on the circle centre O and AB = BC. P is the midpoint of chord AB and Q is the midpoint of chord BC.

(a)Prove that triangle OAP is congruent to triangle OCQ. Give a reason for each statement you make.[3]
(b)Given that obtuse angle COA = 140°, find angle QCO.[2]

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Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

[3] (a) OA = OC radii ∠APO = ∠CQO = perpendicular to chord AP = CQ midpoints [of equal chords] RHS
[3] OR OA = OC radii OP = OQ equal chords [equidistant from centre] AP = CQ midpoints [of equal chords] SSS
[3] OR OP = OQ equal chords [equidistant from centre] ∠APO = ∠CQO = perpendicular to chord AP = CQ midpoints [of equal chords] SAS
[B1] for the correct pair of angles and one correct pair of sides or for two correct pairs of sides
[B1] for correct reason for two pairs of sides/angles
[2] (b) 35°
[B1] for ∠ABC = 70° soi
[B1] or ∠COB = 110° soi
[B1] or ∠COQ = 55° soi
[B1] or ∠OBQ = 35° soi

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