To verify that the angle subtended by an arc at the center of a circle is double the angle subtended at any point on the remaining segment of the circle, we can conduct an experimental procedure. This experiment will provide us with evidence to support the stated theorem.


- A compass
- A ruler
- A protractor
- Drawing paper


1. Draw a circle of any radius on the drawing paper using the compass.
2. Mark a point anywhere on the circumference of the circle and label it as point A.
3. Use the ruler to draw a line segment from the center of the circle to point A. Label this line segment as OA.
4. Measure the length of OA using the ruler and record the value.
5. Without changing the compass width, place the needle on point O and draw an arc across the circle.
6. Mark the points where this arc intersects the circle as B and C.
7. Measure the length of OB and OC using the ruler and record the values.
8. Use the protractor to measure the angle ∠BOC and record the value.
9. Fold the drawing paper along line segment OA so that point A coincides with point C.
10. Place the folded paper on a flat surface and align points O and B.
11. Measure the angle ∠BOC again using the protractor and record the value.
12. Compare the two angles ∠BOC obtained in steps 8 and 11.


- The angle ∠BOC measured in step 8 should be equal to the angle ∠BOC measured in step 11.
- If the two angles are equal, it confirms that the angle subtended by an arc at the center of a circle is double the angle subtended at any point on the remaining segment of the circle.


The experimental procedure involves drawing a circle, measuring the length of the line segment from the center to a point on the circumference, and measuring the angle subtended by an arc at the center of the circle. By folding the paper and comparing the angles before and after folding, we can determine if the angles are equal.

The theorem states that the angle subtended by an arc at the center of a circle is double the angle subtended at any point on the remaining segment of the circle. This can be proven mathematically using the properties of circles and angles. However, this experiment provides a visual and experimental confirmation of the theorem.

By comparing the measurements of the angles obtained in the experiment, we can conclude whether the theorem holds true. If the angles are found to be equal, it supports the theorem, and if they are not equal, it would contradict the theorem.

In this way, the experimental procedure allows us to verify the theorem by providing empirical evidence based on observations and measurements.