Question 12

We will draw a square, find the midpoints of its sides, and then draw arcs from the corners to form the petals.

Step 1 — Draw the square

Let us choose a side length for our square. Draw a straight line segment. Mark points A and B on this line. At point A, draw a line perpendicular to AB. Mark point D on this perpendicular line. Make sure the length AD is equal to AB. At point B, draw another line perpendicular to AB. Mark point C on this line. Make sure the length BC is equal to AB. Finally, join points C and D with a straight line. We have now drawn our square, ABCD.

Step 2 — Find the midpoints of the sides

We need to find the middle point of each side of the square. Use a compass to find the perpendicular bisector of side AB. The point where it crosses AB is the midpoint. Let us call it P. Similarly, find the midpoint of side BC. Let us call it Q. Find the midpoint of side CD. Let us call it R. Find the midpoint of side DA. Let us call it S. These four midpoints are where the petals will touch the sides of the square.

Step 3 — Draw the petals

Now we will draw the arcs that form the petals. Each petal is made of two curved lines, or arcs. There are four petals, so we will draw eight arcs in total.

For the top-left petal (near corner A): Place your compass needle at point D (bottom-left corner). Open the compass so its pencil tip is at point P (midpoint of AB). Draw an arc that starts at P and ends at point S (midpoint of DA). Now, place the compass needle at point B (top-right corner). Open the compass so its pencil tip is at point S. Draw an arc that starts at S and ends at point P.

For the top-right petal (near corner B): Place your compass needle at point A (top-left corner). Open the compass so its pencil tip is at point Q (midpoint of BC). Draw an arc that starts at P and ends at point Q. Now, place the compass needle at point C (bottom-right corner). Open the compass so its pencil tip is at point P. Draw an arc that starts at Q and ends at point P.

For the bottom-right petal (near corner C): Place your compass needle at point B (top-right corner). Open the compass so its pencil tip is at point R (midpoint of CD). Draw an arc that starts at Q and ends at point R. Now, place the compass needle at point D (bottom-left corner). Open the compass so its pencil tip is at point Q. Draw an arc that starts at R and ends at point Q.

For the bottom-left petal (near corner D): Place your compass needle at point C (bottom-right corner). Open the compass so its pencil tip is at point S (midpoint of DA). Draw an arc that starts at R and ends at point S. Now, place the compass needle at point A (top-left corner). Open the compass so its pencil tip is at point R. Draw an arc that starts at S and ends at point R.

You have now drawn all four petals. Erase any extra lines or marks if you wish. This is the required figure with four petals of maximum possible size within the square.