what are the four steps to find the diameter of a circle?

Question

My daughter was told that there is four steps to finding the diameter of a circle. What are the four steps?

Answer 1

D= C/pi

Circumference divided by the pi = diameter

diameter divided by 2= radius

Answer 2

This question doesn't seem to be asking the length of the diameter of a circle, but asking how to draw the diameter, so that the following is a solution for the construction.

To solve this problem, use the fact that the perpendicular bisector  of any chord on a circle passes thru the center of the circle, and the converse is true as well.

1. Draw a horizontal* line that intersects the given circle at 2 points, A and B.   Segment AB is a chord of the circle.

2. Keeping the compass width, approx 3/4 of AB, draw 2 arcs, one from A and the other from B.   They intersect each other at 2 points, C and D, above and below chord AB 

3. Draw a line passing thru 2 intersections, C and D.   Line CD is the perpendicular bisector of  AB.

4. Perpendicular bisector CD intersects the circle at 2 points, E and F above and below AB.   Segment EF is a diameter of the given circle. ** ***

* Any slanted line woud be OK.  The horizontal is just for the convenience.

** This answer may be shortened into 2 steps: 1. drawing a chord,  2. drawing the perpendicular bisector.  

***For the center of the circle, just bisect the diameter, or repeat the same procedure on the other chord. 

 

Answer 3

To draw a diameter of the given circle, use the fact that the angle subtended at any point on the circumference by the diameter, but except 2 points at both ends of the diameter, is a right angle.

1. Draw a horizontal* line intersecting the given circle at 2 points, A and B.   Take care not to draw the line near the probable center.   Segment AB is a chord on the given circle.  

2. Set the compass width to approx 1/2 of AB.   From A, draw an arc intersecting line AB at 2 points, C and D on both sides of A.   Adjust the compass width to approx AC.   Without changing the compass width, draw 2 intersecting arcs, one from C and the other from D.   They intersect each other at 2 points, E and F above and below line AB.  

3. Draw a line that passes thru 2 points E and F, and intersects the circle at point G.  Connect B to G.  

4. Line EF is the perpendicular bisector of segment CD, so that chord AG perpendicular to chord AB, then angle BAG is a right angle.   Therefore, segment BG is a diameter of the given circle.** ***

* any sloped line would be OK.   ** This answer may be shortened into 3 steps: 1. drawing the chord.  2. drawing the perpendicular bisector.  3. connecting B to G.   *** For the center of the circle, just bisect the diameter, or repeat the procedure from B.