How to Locate the Center Point of an Arc

An arc is a segment of a circle. To find the center of an arc is the same as finding the center of the circle it is part of.

Difficulty: Moderately Easy

Instructions

Things You'll Need:

• Compass
• Straight edge
• Paper with an arc drawn on it
• Pen or pencil

Finding the center point of an arc

1. Use the straight edge to draw a straight line from one end of the arc to a point near the arc's mid-point. Call this segment A.

2. Use the straight edge to draw another straight line from the other end of the arc to a point near the arc's mid-point. This point can be the end-point of segment A, but that isn't required. Call this segment B.

3. Anchor the compass on one end of segment A, and draw a half-circle with its mid-point through the other end of segment A.

4. Anchor the compass on the other end of segment A, and draw a half-circle with its mid-point through the first end of segment A. This half-circle should intersect the first half-circle once on each side of segment A.

5. Use the straight edge to draw a line through the two points of intersection between the half-circles. This is the bisector of segment A.

6. Repeat steps 3, 4 and 5 on segment B to draw its bisector.

7. If the two bisectors don't intersect, extend both in the direction that they approach each other until they do intersect. The point at which the bisectors of segments A and B intersect is the center of the original arc.

Tips & Warnings

• Segments A and B are chords in the circle of which the arc is part. The bisector of any chord in a circle goes through the center of that circle.

[starkjoe]

on 1/9/2009 This could also be done in a CAD program