Circle properties and tangentsAQA A-Level Maths: Mind map

Exam questions on Circle properties and tangents

1. 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
2. $AB$ 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
3. 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