CIRCLE THROUGH THREE POINTS

REGULAR PENTAGON ON A GIVEN INSCRIBED CIRCLE

Line tangent to a given point on a circle

Engineering Aid 3 - Beginning Structural engineering guide book
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Figure 4-29.-Regular octagon in a given circumscribed circle. REGULAR OCTAGON IN A CIRCUMSCRIBED CIRCLE GIVEN Figure 4-29 shows a method of constructing a regular octagon in a given circumscribed circle. Draw horizontal diameter AB and vertical diameter CD. Use a T square and a 45° triangle to draw additional diameters EF and GH at 45° to the horizontal. Connect the points where the diameters intersect the circle. REGULAR OCTAGON AROUND A GIVEN INSCRIBED CIRCLE Figure 4-30 shows a method of constructing a regular octagon around a given inscribed circle. Draw horizontal diameter AB and vertical diameter CD. Draw tangents at A, B, C, and D perpendicular to the diameters. Draw the remaining sides of the figure tangent to the circle at 45° to the horizontal. CIRCULAR CURVES Many of the common geometrical con- structions occurring in the drafting room are those involving circular curves. This section explains how to construct circular curves that may be required to satisfy varying conditions. CIRCLE THROUGH THREE POINTS In figure 4-31 the problem is to draw a circle (or a circular arc) that passes through points A, Figure 4-30.-Regular octagon around a circle. given inscribed Figure 4-31.-Circle or arc through three points. B, and C. Connect the points by lines and erect perpendicular bisectors as shown. The point of intersection of the perpendicular bisectors (O) is the center of the circle or arc passing through all three points. LINE TANGENT TO A CIRCLE AT A GIVEN POINT A line that is tangent to a circle at a given point is perpendicular to the radius that intersects the 4-10

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