How to Inscribe a Regular Polygon within a Circle
To inscribe a regular polygon in a circle, divide the full 360 degrees by the number of sides and mark that angle repeatedly around the center. Connecting the marks gives equal sides and equal angles.
Type the problems from this lesson and check each step.
- 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.
Worked examples: inscribing a regular polygon in a circle
Practice questions on inscribed regular polygons
- 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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