Answer:
4. B
5. D
Explanation:
4. Draw a line at angle to the line segment JK.
Then make three arcs on the new line using a compass without changing the setting.
Join the last arc to the endpoint of the line segment (in this case, K) and draw two parallel lines originating from the other two arcs.
5. Recall, there are two lines a and b
where x is the geometric mean.
Draw a line.
Label a point on the line (say, R)
Construct a segment (or arc) with endpoint R and length "a".
Construct a segment (or arc) with length "b" adjacent to the previous segment.
Label the endpoints (say, S and T). The line segment from point RS is "a" and that from point ST is "b".
Construct the perpendicular bisected of segment RT.
Label the midpoint of segment RT.
Using the midpoint as the center and half the length of RT as the radius, construct a semicircle.
At S, construct the perpendicular to segment RT. Label the intersection between the semicircle and perpendicular (say, Y)
SY is the geometric mean.
a/x = x/b is RS/SY = SY/ST