Circles

Question 1

How do you calculate the midpoint of a line segment with endpoints (x1, y1) and (x2, y2)

Answer 1

(x1 + x2 / 2 , y1 + y2 / 2)

Question 2

What is the straight line that is the perpendicular bisector of a line segment AB

Answer 2

The perpendicular bisector of a line segment AB is the straight line that is perpendicular to AB and passes through the midpoint of AB

Question 3

What is the equation of a circle with centre (0,0) and radius r

Answer 3

x^2 + y^2 = r^2

Question 4

What is the equation of a circle with centre (a,b) and radius r

Answer 4

(x - a)^2 + (y - b)^2 = r^2

Question 5

What form can be given to the equation of a circle with the centre: (-f,-g) and radius: square root of f^2 + g^2 - c

Answer 5

x^2 + y^2 + 2fx + 2gy + c = 0

Question 6

What are three ways a straight line can intersect a circle

Answer 6

A straight line can intersect a circle once, by just touching the circle, or twice. Not all straight lines will intersect a given circle

Question 7

How does a tangent intersect a circle

Answer 7

A tangent to a circle is perpendicular to the radius of the circle at the point of intersection

Question 8

How does the perpendicular bisector or a chord intersection a circle

Answer 8

The perpendicular bisector of a chord will go through the centre of a circle

Question 9

If the angle PRQ = 90 then R lies on the circle with diameter PQ. What is the angle in a semicircle

Answer 9

The angle in a semicircle is always a right angle

Question 10

How do you find the centre of a circle

Answer 10

Find the equations of the perpendicular bisectors of two different chords

Find the coordinates of intersection of the perpendicular bisectors