By Chance E. Gartneer Updated Mar 24, 2022
Even when a circle is cut by a straight line, its fundamental properties remain intact. The radius—the distance from the center to the circumference— is a key variable for determining a circle’s size. Whether the remaining segment is more than half or less than half of the whole circle, you can find the radius using simple measurements and basic geometry.
Locate two points on the visible arc that are farthest apart and draw a straight line between them.
Measure the length of this line; it represents the diameter. For example, the line measures 8 centimetres.
Divide the diameter by two to obtain the radius. In the example, 8 cm ÷ 2 = 4 cm.
Measure the straight edge (chord) of the partial circle and square that length. The chord is 7 cm, so 7² = 49.
From the middle of the chord, draw a perpendicular line to the arc and measure its length. In the example, this perpendicular is 2 cm.
Multiply the perpendicular length by 8 and subtract the result from the squared chord value. For instance, 2 × 8 = 16; 49 ÷ 32 = 3.0625.
Halve the perpendicular length and add that value to the result from Step 3. Here, 2 ÷ 2 = 1; 1 + 3.0625 = 4.0625 cm. The radius is 4.0625 cm.
