click below
click below
Normal Size Small Size show me how
circles
chapter 6 - circles
Term | Definition |
---|---|
the midpoint of a line segment (x1,y1) to (x2,y2) | ((x1+x2)/2, (y1+y2)/2) |
the perpendicular bisector of a line segment AB | Is a linear equation that goes through the midpoint of AB and is perpendicular to AB |
equation of a circle centred (a,b) with radius r | (x-a)^2 + (y-b)^2 = r^2 |
expanded form of the equation of a circle | x^2 + y^2 +2fx + 2gy + c = 0 centre (-f,-g) radius sqrt(f^2 + g^2 - c), done via completing the square |
solving intersections of circles and linear functions | done via substitution and, if needed, the discriminant for the number of intersections |
tangents to circles | only intersect the circle once and are perpendicular to the radius at said intersection |
the perpendicular bisector of any chord in a circle | will go through the centre of the circle |
the circumcircle of a triangle | a circle that goes through all 3 vertices |
the circumcentre of the circumcircle | the point at which all 3 perpendicular bisectors of the triangle’s edges meet |
the hypotenuse of a right angled triangle | is the diameter of the circumcircle |