Construct the following figure.

Question

Homi · Accepted Answer

Understand the Question

To construct the given 8-pointed star design:
1. Draw a circle and divide its circumference into 8 equally spaced points using perpendicular diameters and their angle bisectors.
2. Join the vertices by skipping two points at a time (connecting each vertex to the third point clockwise) to form the 8-pointed star outline.
3. Shade the 8 inner triangular regions while leaving the 8 outer star points unshaded.

Step 1 · Draw Base Circle and Divide into 8 Equal Parts

Draw a circle and locate 8 equally spaced points on its circumference. Diagram 1

Draw a circle with center $O$ .
Draw two mutually perpendicular diameters passing through $O$ to mark 4 equally spaced points.
Bisect the angles between these diameters and extend the bisectors to the circumference to obtain 4 more points.
Label these 8 equally spaced points clockwise as $S, T, U, V, W, X, Y, Z$ starting from the top.

Step 2 · Draw Star Outline

Join the points on the circle with straight line segments to form the star. Diagram 2

Draw the following 8 straight line segments:

Step 3 · Identify and Shade Required Regions

Shade the inner triangular regions of the star. Diagram 3

Leave the 8 outer triangular points labeled $A, B, C, D, E, F, G, H$ unshaded (white).
Carefully shade the 8 inner triangular regions forming the body of the star to match the given pattern.

Answer

The 8-pointed star figure is constructed and shaded as required.

Common Mistakes

Unequal Sector Angles: Failing to accurately bisect the $90^\circ$ angles into $45^\circ$ angles, leading to an irregular star shape.
Incorrect Point Connections: Connecting adjacent points (forming an octagon) or skipping the wrong number of vertices instead of connecting each point to the third point clockwise.
Inverted Shading: Shading the outer star tips ( $A$ through $H$ ) instead of the alternating inner triangular regions.

Question 16