A CHORD is a line joining any two points lying ona circle. (CD is a chord of circle O.)An ARC is a portion of the closed curved lineswhich forms the circle. It is designated by CD. An arcis said to be subtended by a chord. Chord CD subtendsarc CD.A TANGENT is a straight line which touches thecircle at one and only one point. (Line MZ is a tangentto circle O.)A CENTRAL ANGLE is an angle whose vertex isthe center of a circle and whose side are radii of thecircle. (As XOY, YOA, and XOB.)CONCENTRIC CIRCLES are circles having thesame center and having different radii.The CIRCUMFERENCE of a circle is the distancearound the circle. It is the distance on the curve from Cto A to X to Y to B to D and back to C.Some examples of problems involving circles ap-plicable to sheet metal work are as follows:1. Construct a tangent to circle O by use of asquare.Solution:Step 1. Place the square in a position so that oneside touches the center and the other sidetouches the circle.Conclusion:A line drawn along the second side will be tangent to thecircle.2. Divide a circle into 6 equal parts.Solution:Step 1. Using a radius of the circle, begin at anypoint, and step off chords equal to theradius. If done accurately, this will make 6divisions of the circle.3. Divide a semicircle into 6 equal parts.Solution:Step 1.Step 2.Step 3.Step 4.At O erect a perpendicular to AB.With point A as the center and radius equalto AO, swing an arc cutting the circle at E.With point B as the center and the sameradius as in step 2, swing an arc cutting thecircle at F.With the same radius, and point C as thecenter, swing arcs cutting the circle at pointsG and H,Conclusion:AG = GE = EC = etc.4. Divide a circle into 8 equal parts.Problem:To divide circle O into 8 equal parts.Solution:Step 1.Step 2.Draw diameter AB. Draw CD perpendicularto AB, thus dividing the circle into 4 equalparts.Bisect the central angle COB. Mark thepoint of the intersection of the bisector andcircle O.AII-8

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