How to Inscribe a Regular Polygon within a Circle
- A straightedge or ruler for accurate linear measurements.
- A compass for drawing the circle and aiding in polygon construction.
- A pencil for drawing and annotations.
Examples
Practice Questions:
- What would be the central angle for a regular decagon (\(10\) sides)?
- How many vertices will touch the circle if a regular pentagon is inscribed in it?
- For a given central angle, can you determine the number of sides of the inscribed regular polygon?
- For a decagon, the central angle is \( \frac{360^\circ}{10} = 36^\circ \).
- A regular pentagon has \(5\) vertices, so all 5 vertices will touch the circle.
- Yes, using the formula \( n = \frac{360^\circ}{\text{Central Angle}} \). The value of \( n \) will give the number of sides of the polygon.
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