Let’s talk about what you need to know for Coordinate geometry, circles (in coordinate geometry) and proofs in plane geometry for O Level Additional Mathematics.

### Coordinate geometry

- finding the gradient of a straight line from 2 given points
- finding distance between 2 points
- finding the midpoint of 2 points
- finding the equation of a straight line
- relationship between gradients when the straight lines are parallel or perpendicular
- finding the equation of the perpendicular bisector
- finding area using shoe-lace method

### Circles in coordinate geometry

- equation of circles in the following form:
- (x-a)
^{2}+ (y-b)^{2}=r^{2} - x
^{2}+ y^{2}+ 2gx + 2fy +c = 0

- (x-a)
- problems involving circles and coordinate geometry

### Proofs in plane geometry

- proofing similar and congruent triangle (also tested in elementary mathematics)
- mid-point theorem
- alternate angles and corresponding angles
- alternate segment theorem and other geometric properties of circles (e.g. angle in the same segment, angle in a semi- circle, the angle at the centre of circle, etc.)

A lot of concepts are covered in the topics on coordinate geometry, circles and proofs in plane geometry. I go through in detail the concepts and how to tackle questions from these chapters in my complete course on Coordinate Geometry, Circles, and Proofs in plane geometry which you can get here.