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  • How to Divide a Circle into Three Equal Parts: A Practical Geometry Tutorial

    By Kevin Beck | Updated Aug 30, 2022

    Circles appear everywhere—from celestial bodies to everyday objects. Whether you're slicing pie, planning a garden, or creating artwork, knowing how to split a circle into equal segments is a useful skill.

    Step 1: Draw a Diameter

    Using a straightedge, draw a straight line through the circle that touches both edges. This line is the diameter and automatically divides the circle in half.

    Step 2: Locate the Center

    Find the midpoint of the diameter by halving its length. Mark this point; it is the center of the circle.

    Step 3: Mark the Quarter Point (Point A)

    From the center, measure exactly one‑fourth of the diameter (or half the radius) toward one edge. Mark this point A.

    Step 4: Draw a Perpendicular Through Point A

    Using a protractor or a right‑angle template, draw a line through A that is perpendicular to the diameter. Extend this line to intersect the circle at points B and C.

    Step 5: Connect the Center to B and C

    Draw straight lines from the center to points B and C. These are radii of the circle.

    Step 6: Verify the 120° Segments

    The two right triangles formed inside the circle are 30°–60°–90° triangles, because the short leg equals half the hypotenuse (the radius). As a result, the central angles between the radii and the diameter are each 120°, giving three equal sectors.

    With this method, you can confidently divide any circle into three equal parts for cooking, design, or mathematical work.

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