With an aid of diagram construct a regular pentagon within a circle of diameter 70mm?

To construct a regular pentagon within a circle of diameter 70mm, follow these steps:

1. Draw a circle with a diameter of 70mm.

2. Draw a horizontal line through the center of the circle.

3. Use a protractor to mark 72-degree angles at the top and bottom of the circle.

4. Draw lines from the top and bottom points to the center of the circle.

5. Repeat steps 3 and 4 to mark 72-degree angles at the remaining points where the lines intersect the circle.

6. Connect the points where the lines intersect the circle to form a regular pentagon.

Your diagram should now show a regular pentagon inscribed within the circle of diameter 70mm.

Step 1: Draw the Circle

- Using a compass, draw a circle with a diameter of 70 mm.

Step 2: Divide the Circle into Five Equal Parts

- Divide the circle into 5 equal parts using a protractor or compass. Mark the points A, B, C, D, and E.

Step 3: Draw the Chords

- Draw chords AB, BC, CD, DE, and EA. These chords will intersect each other at a point, F.

Step 4: Connect the Intersection Point to the Points on the Circle

- Connect point F to points A, B, C, D, and E. These lines will form the sides of the regular pentagon.

Diagram:

[Image of a circle with a diameter of 70 mm divided into five equal parts. Chords AB, BC, CD, DE, and EA are drawn, intersecting at point F. Lines are then drawn from F to points A, B, C, D, and E, forming the regular pentagon.]

Verification:

- The five sides of the pentagon are equal in length, as they are formed by the chords of the circle.
- The five interior angles of the pentagon are equal to 108 degrees each, as the sum of the interior angles of a regular pentagon is 540 degrees.