O-LevelMathematicsGeometry4024/22 · Oct/Nov 2019 · Q1010 Marks

AC and BD are diameters of the circle, centre O. Show that triangle ABC is congruent to triangle BAD. Give a reason for each statement you make.

(a)AC and BD are diameters of the circle, centre O. Show that triangle ABC is congruent to triangle BAD. Give a reason for each statement you make.[3]
(b)(i)Two tangents, TC and TD, are drawn to the circle in part (a). The diameter of the circle is 8cm and ABD = 28°. Find CÔD.[2]
(b)(ii)Calculate the area shown shaded in the diagram.[5]

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 2019). The mark or mark type is shown in brackets.

[3] AC=BD equal diameters
[3] AB is common
[3] ∠ABC = ∠BAD = 90° angle in semicircle
[3] Congruent RHS
[3] B1 for correct pair of angles and one correct pair of sides or for two correct pairs of sides
[3] B1 for correct reasons for two pairs of sides/angles
[2] 124°
[2] B1 for ∠ADB or ∠BCA = 62° soi or ∠AOD = 56° soi or ∠AOB = 124° soi
[5] 12.8 or 12.77 to 12.78
[5] M4 for 4×4tan(their 124/2) – (their 124/360)×π×4^2 oe
[5] OR M1 for DT = 4 tan(their 124/2) oe
[5] or OT = 4/cos(their 124/2) oe
[5] M1 for [area kite =] 4×their DT oe or their OT × 4 sin(their 124/2) oe
[5] M1 for [sector area =] (their 124/360)×π×4^2 oe

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