PROPOSITIONS OF GEOMETRY Table 2c. Geometric Constructions Machinery's Handbook, 31st Edition
68
C
To draw a circular arc with a given radius through two given points A and B : With A and B as centers, with the compass draw two circular arcs with the given radius intersecting at C . With C as center and the same radius, draw a circular arc through A and B .
A
B
To locate the center of an arc of a circle: Select three points on the periphery of the circle, as A , B , and C . With each of these points as a center and setting the same radius with the compass, draw arcs intersecting each other. Through the points of intersection, draw lines DE and GF . Point H , where these lines intersect, is the center of the circle.
H
C
G
D
F
A
B
E
E
C
To draw a tangent to a circle through a given point on the circumference: Through a chosen point of tangency A on a circle with center B , draw radius BC . At point A , draw a line EF at right angles to BC . This line is the required tangent.
A
F
B
C
To divide a circular arc AB into two equal parts: With A and B as centers, and a radius larger than half the distance between A and B , with the compass draw circular arcs intersecting at C and D . Line CD divides arc AB into two equal parts at E .
A
B
E
D
C
To circumscribe a circle about a triangle ABC : Bisect the sides AB and AC , and from the midpoints E and F draw lines at right angles to the sides. These lines intersect at G . With G as a center and GA as a radius, draw circle ABC .
F
G
B
A
E
B
To inscribe a circle in a triangle ABC : Bisect two of the angles, A and B , by lines intersecting at D . From D , draw a line DE perpendicular to one of the sides, and with DE as a radius, use the compass to draw circle EFG .
E
F
D
A
G
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