Circle Theorems — Questions

IGCSE Mathematics (0580) practice questions. Work through each question before checking the solutions page.

Question 1

[2](a)An angle at the circumference is 35°. State the size of the angle at the centre standing on the same arc.

Question 2

[2](a)ABCD is a cyclic quadrilateral. Angle A = 108°. Calculate angle C.

Question 3

[1](a)State the angle between a tangent to a circle and the radius drawn to the point of contact.

Question 4

[1](a)State the size of the angle in a semicircle.

Question 5

[2](a)A tangent-chord angle is 48°. State the angle in the alternate segment.

Question 6

[2](a)ABCD is a cyclic quadrilateral with angle B = 95°. Calculate angle D.

Question 7

[2](a)An angle at the circumference is 42°. Find the angle at the centre standing on the same arc.

Question 8

[1](a)State the relationship between the lengths of two tangents drawn from the same external point to a circle.

Question 9

[1](a)State what a perpendicular line from the centre of a circle to a chord always does to that chord.

Question 10

[1](a)Two angles in the same segment of a circle stand on the same arc. State the relationship between them.

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