Explore the distances from an interior point of an octagon to its sides. What is the sum of these distances?
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Drag point Q to new locations within the octagon to investigate the distances to each side. (Note: if point Q is moved beyond the sides, some of the measurements will disappear.) To change the size of the octagon, click-and-drag point X.
Choose Trace Path of Q to trace the path of point Q as it is moved. To erase the path, click the red X in the lower right corner of the applet.
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Choose Trace Path. Then, slowly and carefully drag Q through the interior of the octagon so that all eight segments (AQ‑FQ) are visible. If any segments disappear, move back toward the interior so that they reappear.
- Describe the region through which Q can move so that none of the segments disappear.
- Explain why this happens.
- How is the region determined? Why does it have the shape it has?
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