Pass Check: Circle Theorems
Learn all circle theorems by name and use them with clear angle reasons in proofs.
Tangent
A straight line that touches a circle at exactly one point and is perpendicular to the radius at that point.
Chord
A straight line joining two points on the circumference.
Cyclic quadrilateral
A four-sided shape with all corners on the circumference of a circle.
Subtend
An arc or chord 'subtends' an angle at a point, meaning it creates that angle when lines are drawn from its ends to that point.
Quick check
Mixed quiz
1. A triangle is inscribed in a semicircle with the diameter as one side. What type of triangle is guaranteed regarding one of its angles?
2. In a circle, angle BAC=90° where BC is a chord (not necessarily the diameter) and A is on the circle. What can you conclude about BC?
3. Which theorem states that the angle at the centre is twice the angle at the circumference subtended by the same arc?
4. In a right-angled triangle the hypotenuse is 10 cm and one angle is 60 degrees. Find the length of the side opposite this angle, to 1 decimal place.
5. A right-angled triangle has opposite side 11 cm and adjacent side 13 cm. Find the angle, to 1 decimal place.
6. In a right-angled triangle the hypotenuse is 10 cm and one angle is 30 degrees. Find the length of the side opposite this angle, to 1 decimal place.
7. In a right-angled triangle the hypotenuse is 10 cm and one angle is 45 degrees. Find the length of the side opposite this angle, to 1 decimal place.
8. Which ratio connects adjacent and hypotenuse?