Use the circle below. a. What appear to be the minor arcs of OL?
b. What appear to be the semicircles of OL?
c. What appear to be the major arcs of OL that contain point K?

a. IH and JK

b. IK and HJ

c. HK

Step-by-step explanation:

IH and JK are the minor arcs because the other arcs (IJ and HK) are major arcs. They (IH and JK) are minor arcs because they are acute angle and the other arcs are Obtuse.

IK and HJ are semicircles because they are two points that is forming a line between the circle. two points that are connected, is already a semicircle.

HK is a major arc because it's central angle is obtuse.

  5.   y=6; de=7; fg=8

  6.   x=4.2; jl=14.2; mn=13

step-by-step explanation:

when chords cross inside a circle, the product of the segment lengths is a constant.

5. dh×eh = fh×gh

  y = gh = dh×eh/fh = 3×4/2 . . . divide by the coefficient of gh

  y = 6

of course, the total chord length is the sum of the lengths of its segments.

  de = dh +eh = 3+4 = 7

  fg = fh +gh = 2+6 = 8

6. this problem works the same way as the previous one.

  x = lk = mk×nk/jk = 6×7/10 = 4.2

  jl = jk +lk = 10 +4.2 = 14.2

  mn = mk +nk = 6 +7 = 13

comment on chords and secants

you can think of the points h (problem 5) and k (problem 6) as points where the chords meet. a chord is part of a secant line, a line that intersects the circle in two points. one can also consider these points (h or k) to be the points where the respective secant lines meet.

then, the product that is a constant is the product of the distance from the meeting point (h or k) to one circle intersection with the distance from that meeting point to the other circle intersection. for problem 5, the constant is the product hd×he = hf×hg.

it turns out that this rule regarding the products of lengths to points of intersection is also true when the secants intersect outside the circle.

that is, you only need to remember one rule to work both kinds of problems.

for b its (t) and c its (d)

step-by-step explanation: