Take this Quiz: GCSE Maths: Circle Theorems (Higher) | Zestly

Question 1

In a circle with center O, points A, B, and C lie on the circumference. If the angle at the center, $\angle AOC$, is $110^\circ$, what is the measure of the angle at the circumference, $\angle ABC$, assuming B is on the major arc AC?

Accepted Answer

$55^\circ$

Question 2

Points A, B, C, and D lie on the circumference of a circle in that order. Which of the following statements regarding the angles of the cyclic quadrilateral ABCD are true?

Accepted Answer

$\angle ABC + \angle ADC = 180^\circ$

Question 3

A line segment AB is a diameter of a circle with center O. Point C is any other point on the circumference. What is the measure of $\angle ACB$?

Accepted Answer

$90^\circ$

Question 4

A tangent to a circle at point P meets the radius OP. What is the angle between the tangent and the radius at the point of contact?

Answer

$45^\circ$

Answer

$180^\circ$

Answer

$90^\circ$

Answer

$0^\circ$

Question 5

Two tangents are drawn to a circle from an external point P, touching the circle at points A and B. Which of the following properties are true?

Answer

The lengths of PA and PB are equal.

Answer

The line segment OP bisects $\angle APB$.

Answer

$\angle OAP = 180^\circ$

Answer

The triangle OAP is equilateral.

Answer

The length of PA is twice the radius.