11 self-marking GCSE practice questions on The angle in a semicircle, written specifically for AQA, Pearson, OCR across Higher tier. Instant marking with full worked solutions on every question.
A few of the 11 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.
Question 12 marksGrade 6-7
A, B and C are points on the circumference of a circle, and AB is a diameter. Angle BAC=40°
What are the common mistakes in The angle in a semicircle?
When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.
Confirms the result holds for one diagram rather than proving it generally
Measured or checked a single drawn diagram rather than proving the result algebraically holds for every position of the third point on the circumference - a specific example or measurement is not a proof
Doesn't use the fact that the angle in a semicircle is always 90°
Forgot that the angle in a semicircle is 90°, and instead used only the triangle angle sum with the given angle (180 - knownAngle) rather than subtracting the 90° angle too
Cites the result as a known theorem instead of constructing the required first-principles proof
States "angle in a semicircle is 90° by the circle theorem" as if this were a valid proof, when the question explicitly requires proving the result from first principles WITHOUT citing any circle theorems.
Quick answers about The angle in a semicircle
How many The angle in a semicircle practice questions are there?
There are 11 self-marking GCSE Maths questions on The angle in a semicircle, written for AQA, Pearson, OCR across Higher tier. Each one is marked instantly and has a full worked solution.
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.
(a) Find the size of angle
ABC
.
(b) Give a reason for your answer.
Show the worked solution
AB is a diameter, so the angle at C on the circumference (angle ACB) is subtended by a semicircle. The angle in a semicircle is always 90°, so angle ACB=90°. M1
Angles in a triangle sum to 180°, so angle ABC=180−90−40=50°. A1
Question 23 marksGrade 8-9
O is the centre of a circle, and AB is a diameter. C is a point on the circumference. Prove that angle ACB=90° for any position of C on the circumference (the angle in a semicircle is a right angle).
Show the worked solution
Draw radius OC. Since OA, OB and OC are all radii, triangles OAC and OBC
Question 35 marksGrade 9
A, B and C are points on the circumference of a circle, centre O. AOB is a diameter of the circle.
Prove that angle ACB is 90°. You must not use any circle theorems in your proof.