Edexcel IGCSE Math B 6.K Circle theorems Question Bank

Practise applying circle theorems, tangents, chords and sectors to calculate angles, lengths, radii and areas from diagrams.

Exam points

calculate unknown angles using centre-circumference, tangent-radius and chord facts
apply intersecting chord or tangent length relationships to find missing lengths or radii
combine sector area, trigonometry or sine rule steps with circle geometry in diagrams

[Maximum number: 3]

Diagram NOT accurately drawn

Figure 3 shows a circle with centre O and radius 10 cm.
The points A and B lie on the circle such that $\angle A O B=100^{\circ}$ The point C is such that AC and BC are tangents to the circle.

Giving reasons, calculate the size, in degrees, of $\angle A C B$ .

$\angle OAC=\angle OBC=90^\circ$ $\angle ACB=80^\circ$
Reasons may use tangent-radius angles and angles in a quadrilateral, or split into two triangles using tangent, triangle angle sum, and the isosceles/bisector facts.

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6.K Circle theorems question 1