Circle Flashcards
What is the general equation/algebraic form of a circle?
x² + y² = r²
This is where the centre of the circle is at the origin (0,0)
How do you find the area of a circle?
A = π r²
How do you find the perimeter/circumference of a circle?
C = 2 π r
OR
C = π d
What two things do you need to prove that the equation of a circle with centre (0,0) is x² + y² = r²?
-A right angle triangle
-Pythagoras Theorem
What is the equation of a circle whose centre is (a,b)?
(where the centre is not the origin)
(x-a)² + (y-b)² = r²
This is known as the ‘fully general equation of a circle’
To get the expanded form of a circle back into the general form of a circle, what process is required?
Completing the square
How do we find the points of intersection of a line and a circle?
By solving their equations simultaneously
What does it mean if a line which passes through the centre of the circle meets or intersects a tangent at the circumference of a circle?
The lines meet or intersect at a right angle
What does it mean if a line which passes through the centre of the circle bisects a chord?
The line bisects the cord at a 90 degree angle
What do we call any line that cuts another line into two equal halves?
A bisector
What do we call a line that cuts another line at a right angle into two equal halves?
A perpendicular bisector
What formula can we use to find the distance between two coordinates?
d=√((x2 – x1)² + (y2 – y1)²)
This formula can be used as another method to find the radius of a circle when given the centre and a point on the circumference.
What do we call a circle that contains a triangle and has all of the triangle’s vertices on its circumference?
A circumcircle
What is true for every triangle?
For every triangle, there is a unique circle that can be drawn around it, which passes through the points of all three of the triangle’s vertices.
