Construct a regular pentagon in a circle of radius 3.6cm.

To construct a regular pentagon inscribed in a circle with a radius of 3.6 cm, follow these detailed steps:

Materials needed:
Compass
Ruler
Protractor (optional)
Steps to construct the regular pentagon:
Draw the circle:

Use the compass to draw a circle with a radius of 3.6 cm. Place the compass pointer at the center of the circle and adjust the pencil part to 3.6 cm. Draw the circle.
Mark the center:

Label the center of the circle as O.
Divide the circle into 5 equal parts:

To divide the circle into 5 equal parts, we need to calculate the central angle for each segment. The total angle around a point is 360°, and since there are 5 sides in the pentagon, the central angle for each side is:
360° ÷ 5 = 72°.
Mark the first point:

Draw a horizontal line from the center O to the edge of the circle. This line will serve as the reference for measuring the angles.
Mark the point where the line intersects the circle as A. This is the first vertex of the pentagon.
Construct the other vertices:

Using a protractor, place the center at O and measure a 72° angle from the horizontal line to the right.
Mark the point where this line intersects the circle as B.
Repeat this process, measuring a 72° angle from each new line to find the remaining points of intersection on the circle. The next points will be C, D, and E.
Connect the vertices:

Use a ruler to draw straight lines connecting the consecutive points: A to B, B to C, C to D, D to E, and finally E to A.
You have now constructed a regular pentagon inscribed in a circle with a radius of 3.6 cm.