O-LevelMathematicsGeometry4024/12 · Oct/Nov 2025 · Q144 Marks
A, B, C and D are points on a circle, centre O. EF is a tangent to the circle at A. Angle BAF = 65° and angle AOD = 80°. Find angle BCD. Give a geometrical property to explain each step of your working. [Figure: Circle with points A,B,C,D, centre O. Tangent EF at A. Angles BAF=65, AOD=80 shown. NOT TO SCALE]
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- [4] [∠ BCD = ] 105°
- [4] B2 B1 for ∠BCA = 65° or for ∠ACD = 40°
- [4] B1 Dep on ∠BCA = 65° (alternate segment theorem associated with ∠BCA)
- [4] B1 Dep on ∠ACD = 40° (Angle at the centre is twice the angle at the circumference associated with ∠ACD)
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