10 questions🇬🇧English
🔵 Circle Theorems – GCSE
Maths · GCSE — applying the circle theorems to find missing angles and give correct reasons
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Questions
A triangle is drawn inside a circle so that one side is a diameter. What is the angle opposite the diameter?
180°
60°
45°
90°
20s
A tangent touches a circle at point A. What angle does it make with the radius drawn to A?
180°
45°
60°
90°
20s
In a cyclic quadrilateral, what do the two opposite angles add up to?
180°
270°
360°
90°
20s
An arc subtends an angle of 35° at the circumference. What angle does the same arc subtend at the centre?
35°
17.5°
145°
70°
20s
ABCD is a cyclic quadrilateral. Angle DAB = 112°. What is angle BCD?
248°
56°
112°
68°
30s
A, B, C, D lie on a circle, with C and D on the same side of chord AB. Angle ACB = 40°. Why is angle ADB also 40°?
Angles in the same segment are equal
Angle at centre is twice angle at circumference
Angle between tangent and chord theorem
Opposite angles in a cyclic quadrilateral
30s
PA is a tangent to a circle with centre O, touching it at A. OA = 5 cm and OP = 13 cm. How long is PA?
18 cm
12 cm
8 cm
10 cm
30s
A tangent touches a circle at A. The angle between the tangent and chord AB is 65°. C is on the circle in the alternate segment. Find angle ACB.
115°
65°
130°
25°
30s
Tangents from point P touch a circle, centre O, at A and B. Angle APB = 50°. Find angle AOB.
50°
100°
140°
130°
60s
O is the centre. A, B, C lie on the circle with C on the minor arc AB. Angle AOB = 120°. Find angle ACB.
240°
120°
60°
30°
60s