Do you still remember all the properties of circles in IGCSE/GCSE Maths?
Properties of Circles
1. Perpendicular bisector of any chord always passes through the centre of the circle.
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4936730/871276_372610.png)
2. Where a tangent meets a radius the angle between them is always 90º.
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4936730/989529_589983.png)
3. Tangents from same point are always equal in length to where they touch the circle.
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4936730/182624_437529.png)
4. An angle in a semi circle is always 90º (When a triangle goes through the centre, where it hits the circumference = 90º).
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4936730/978193_157650.png)
5. The angle subtended at centre is twice angle at circumference.
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4936730/399560_32515.png)
6. Angles in the same segment, subtended by the same arc/chord are equal.
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4936730/694972_296774.png)
7. Opposite angles of a cyclic quadrilateral add to 180º/supplementary.
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4936730/887924_508047.png)
8. Alternate Segment theorem ⟶ the angle between a tangent and a chord is equal to the angle subtended by the chord in the alternate segment.
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4936730/232228_761078.png)
That's the end of the topic!
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4936730/499090_946043.png)
Drafted by Bonnie (Mathematics)