1. Day 42 – Square inscribed in a circle

2. Introduction
Inscribing a figure into a circle implies drawing a circle so that it touches the vertices of the figure. This concept is important especially in the design of moving parts of a machine. We may have a square like gadget of fitting that rotates about the center. For it to move freely, an allowance equal to a circle swept when its vertices moves have to be left. In this lesson, we are going to learn how to draw a square inscribed in a circle.

3. Vocabulary
Circle
The path of a point that moves at an equal distance from a point that is fixed called the center of the circle.
Square
A four-sided geometric plane figure whose sides are all equal.

4. Construction We first draw a circle To draw a circle, of radius, say 1
Construction We first draw a circle To draw a circle, of radius, say 1.5 inches, identify a point, call it P. This will be the center of the circle. Put the tip of the compass at P then open it to a radius of 1.5 in then draw a complete arc. To draw the inscribed square Draw a straight line from the one side of the arc to the other through P. Name endpoints of the line as A and C respectively. AC is the diameter circle.

5. We the draw a perpendicular bisector to AB
We the draw a perpendicular bisector to AB. We let the bisector intersect the arc above AC at D and below AC at B. P A C

6. We the connect the points A,B,C and D to get a square ABCD.

7. Thus, the final figure. P A C B D

8. Exercise 1 Draw an inscribed square in a circle of diameter 2 in
Exercise 1 Draw an inscribed square in a circle of diameter 2 in. Solution Since the diameter is 2 in, the radius is 1 in. We then draw a circle of radius 1 in the draw a diameter in any direction.

9. We the draw the perpendicular bisector of the diameter and let it intersect the arcs of the circle. We then connect the points of the perpendicular lines intersecting the arc to get a circle.

10. homework
Draw a square inscribed in a circle of radius 3.5 in.

11. Answers to homework
Answer

12. END