Circles

Question 1

What is the midpoint of a line segment?

Answer 1

The point that divides the segment into two equal parts

Midpoint is calculated using the coordinates of the endpoints.

Question 2

What is the perpendicular bisector of a line segment AB?

Answer 2

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

This line divides the segment into two equal lengths at a right angle.

Question 3

If the gradient of AB is m, what is the gradient of its perpendicular bisector?

Answer 3

-1/m

The gradient of the perpendicular bisector is the negative reciprocal of the gradient of the line segment.

Question 4

equation of circle with centre (0,0)

Answer 4

x² + y² = r²

Question 5

equation of circle with centre (0,0)

Answer 5

x² + y² = r²

Question 6

equation of circle with centre (a, b)

Answer 6

(x - a)² + (y - b)² = r²

Question 7

how many times does a straight line intersect with a circle

Answer 7

either once, twice, or not at all.

Question 8

feature of a tangent to a circle

Answer 8

line is perpendicular to the radius of the circle at the point of intersection

Question 9

how to find the centre of a circle if given any 3 points

Answer 9

1. find equations of the perpendicular bisectors of the two different chords
2. find coordinates of intersection of the two perpendicular bisectors

Question 10

triangle PRQ is in a semicircle, if angle <PRQ = 90°, what does this tell us

Answer 10

R lies on the circle with diameter PQ.