Chapter 6 - Circles Flashcards
How do you find the midpoint of a line segment with both end coordinates? (x1 , y1) and (x2 , y2).
( (x1 + x2)/2 , (y1 + y2)/2 )
What is the perpendicular bisector of a line AB?
It is the straight line that is perpendicular to the line AB and passes through the midpoint of AB.
What is the equation of a circle with the centre (0 , 0) and the radius r.
x2 + y2 = r2.
What is the equation of a circle with the centre (a , b) and radius r?
(x - a)2 + (y - b)2 = r2.
How do you find the centre and radius of a circle if it is written like:
x2 + y2 + 2ax + 2by + c = 0?
Complete the square for x and y separately.
(x + a)2 + (y + b)2 = a2 + b2 - c
Centre= (-a, -b) Radius= square root of (a2 + b2 - c)
How many different ways can a line touch a circle and describe them.
It can touch the circle in 2 different ways.
- Just touching the circle at one point ie tangent
- Touching the circle at two points ie chord
- Not touching the circle at all.
What is special about a tangent to a circle?
It is perpendicular to the radius of the circle at the point of intersection.
Tangent and radius are perpendicular so gradients are m and -1/m
What is special about the perpendicular bisector of a chord?
It always goes through the centre of the circle.
What is the size of the angle PRQ if R lies on the circle and PQ is the diameter? What is the circle theorem that fits this?
It is 90* (a right-angle). The angle in a semicircle is always a right angle.
How do you find the centre of a circle when given 3 points that lie on the circle?
Find the equations of the perpendicular bisectors of 2 of the chords. Then find the coordinates of the intersections of the two perpendicular bisectors.
