Circle propertiesEdexcel International A Level Maths: Mind map

Exam questions on Circle properties

1. A circle has diameter $AB$, where $A=(1,2)$ and $B=(9,8)$. The point $P=(8,1)$ lies on the circle.
   Show that angle $APB$ is a right angle, and name the circle property you are using.2 marks
2. A circle has centre $C=(2,3)$ and radius $5$. The points $P=(5,7)$ and $Q=(6,0)$ lie on the circle.
   Find the exact distance from $C$ to the chord $PQ$.2 marks
3. The circle $S$ has equation $(x-1)^2+(y+2)^2=25$. The point $T=(4,2)$ lies on $S$.
   Find an equation of the tangent to $S$ at $T$, giving your answer in the form $ax+by+c=0$ where $a$, $b$ and $c$ are integers.3 marks