U2C1: Special Segments in Circles

Question 1

locus

Answer 1

a set of points

Question 2

locus theorem 1

Answer 2

the locus of points at a fixed distance, d, from a point p is a circle with the given point p as its center and d as its radius

Question 3

equation of a circle

Answer 3

(x - h)^2 + (y - k)^2 = r^2

basically the distance formula

(h, k) is the center of the circle

Question 4

locus theorem 2

Answer 4

the locus of points at a fixed distance, d, from a line, l, is a pair of parallel lines both a distance, d, from l

Question 5

chord

Answer 5

a line segment connecting any point on a circle to any other point on the circle

Question 6

property of intersecting cords

Answer 6

chords intersect = 4 segments created

product of lengths of the two segments from one chord = product of lengths of the two segments from other chord

Question 7

property of chords and their distance from the center of the circle

Answer 7

two chords in the same circle are the same distance away from the center of the circle if and only if they are the same length

Question 8

property of chords perpendicular to a segment in a circle

Answer 8

a chord is perpendicular to a segment that goes through the center of a circle if and only if that chord is bisected