Circle properties and tangentsAQA A-Level Maths: Flashcards

What these 12 flashcards ask

What is the angle in a semicircle?
How do you test whether A\hat{P}B=90^\circ using coordinates?
If P is inside the circle with diameter AB, what is A\hat{P}B?
What does the perpendicular from the centre do to a chord?
Where does the perpendicular bisector of a chord pass?
Right-angled triangle formed by the centre, a chord's midpoint and a chord end?
How is a tangent related to the radius at the point of contact?
How do you find the tangent gradient at T?
Steps to find the equation of a tangent at T?
If the tangent at T is horizontal, what can you say about the radius at T?
Length of a tangent from an external point P?
How many points does a tangent share with the circle?

Exam questions on Circle properties and tangents

A circle has centre $C(1,2)$ and passes through the point $A(5,5)$ .
Find the equation of the tangent at $A$ , in the form $ax+by+c=0$ where $a$ , $b$ and $c$ are integers.2 marks
$AB$ is a diameter of a circle, where $A(-1,1)$ and $B(7,5)$ .
Find the equation of the circle with diameter $AB$ .2 marks
A circle has centre $O(2,3)$ and radius $5$ . The points $P(-1,7)$ and $Q(6,0)$ lie on the circle, and $M$ is the midpoint of the chord $PQ$ .
Find the coordinates of $M$ and show that $OM$ is perpendicular to $PQ$ .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).