Circle theorems and constructionsIB MYP Maths Extended: Flashcards

What these 13 flashcards ask

Angle at the centre compared with the angle at the circumference?
Angle in a semicircle?
Angles in the same segment?
Opposite angles of a cyclic quadrilateral?
A tangent meets a radius at what angle?
Tangents from an outside point?
Why is a triangle made of two radii and a chord isosceles?
What is a chord?
What is a cyclic quadrilateral?
Centre angle 116^\circ. Angle at circumference?
How do you construct a perpendicular bisector?
How do you construct an angle bisector?
How do you find the centre of a circle with a compass?

Exam questions on Circle theorems and constructions

$A$ , $B$ and $C$ are points on the circumference of a circle with centre $O$ . $C$ is on the major arc $AB$ and angle $AOB=116^\circ$ .
$D$ is a point on the minor arc $AB$ . Find the size of angle $ADB$ , giving a reason.2 marks
$PQ$ is a diameter of a circle with centre $O$ . $R$ is a point on the circle and angle $RPQ=35^\circ$ . The line $QT$ is the tangent to the circle at $Q$ , and $T$ is on the same side of $PQ$ as $R$ .
Find the size of angle $RQT$ , giving a reason for each step.2 marks
Two tangents $TA$ and $TB$ are drawn from a point $T$ outside a circle with centre $O$ . They touch the circle at $A$ and $B$ . Angle $ATB=50^\circ$ .
Find the size of angle $TAB$ . Give a reason for each step.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).