Circles

Question 1

general formula of a circle

Answer 1

(x-x1)+(y-y1)=r²

Question 2

if the diameter AB forms a triangle ABC with C at a point on the circle then what angle is 90°?

Answer 2

angle BAC (with diameter as the hypothenuse)

Question 3

what is the relationship between a chord and a radius?

Answer 3

the radius perpendicularly bisects the chord

Question 4

how would you work out how many times a line intersects a circle?

Answer 4

solve the circle and like equation simultaneously and use the discriminant:

• b²-4ac<0, line DOES NOT intersect
• b²-4ac=0, line is a TANGENT
• b²-4ac>0, line intersects TWICE

Question 5

how would you tell if point P lies inside or outside of the circle?

Answer 5

• (CP)² < r², P is inside circle
• (CP)² = r², P is on circle
• (CP)² > r², P is outside of circle

Question 6

what is the relationship between tangents to a circle from the same point (off the circle)?

Answer 6

they are equal lengths