Question 197065: What are the steps for inscribing an equalateral triangle in a circle by means of constructions? Found 2 solutions by RAY100, Mathtut:Answer by RAY100(1637) (Show Source):
You can put this solution on YOUR website! Inscribing any triangle requires finding the intersection of the angle bisectors of the triangle. This is the center of the inscribed circle,
To bisect any angle, draw any arc with vertex as center, and intersect both sides of angle.
From each of these intersections draw an equal arc to make another intersection.
Connect this second intersection with the vertex for the angle bisector.
For the triangle do this for each angle to find center of the inscribed circle.
For the ciircumscribed circle on a triangle, use perpendicular bisectors of each side to
find center of that circle at their common intersection.
Perpendicular bisectors are found by drawing common arcs from each end of the side (vertices)
and the connecting the intersections of the arc.
You can put this solution on YOUR website! Draw a circle.
Label a point on the circle, point A.
With the compass on A and the radius equal to that of the circle draw an arc intersecting the circle at two other points B and C.
Draw segment BC and with compass on B with radius equal to BC, draw another arc intersecting the circle at point D.
Draw BD and CD.
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Draw a circle. Keep the radius of your compass fixed!
Starting anywhere on the circumference, mark off steps with your compass and pencil round your circle. If you do it accurately, it should fit exactly six times around.
Joining alternate points with your straight edge will give you the triangle. {Remember no measuring!}
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