why is it possible to draw a circle which passes through all vertices of a rectangle
Any point on the perpendicular bisector of each side is equidistant from the two vertices involved. Therefore the intersection of these is equidistant from all. Thus the center of the "circumcenter" is at the intersection of perpendicular bisectors. See:
http://en.wikipedia.org/wiki/Circumscribed_circle
To draw a circle that passes through all the vertices of a rectangle, it's important to first understand the properties of a rectangle and a circle.
A rectangle is a quadrilateral with four right angles. Any two opposite sides of a rectangle are congruent, meaning they have the same length. The diagonals of a rectangle bisect each other and are congruent.
On the other hand, a circle is a geometric shape with all points equidistant from its center. It is defined by its center and radius.
Now, let's consider a rectangle and how it is possible to draw a circle passing through all of its vertices:
1. Draw a rectangle: Start by drawing a rectangle on a piece of paper. You can use a ruler to ensure that the sides are straight and the angles are right. Label the vertices as A, B, C, and D.
2. Locate the midpoint of a diagonal: Choose any diagonal of the rectangle (either AD or BC). Using a ruler or by estimating visually, locate the midpoint of the chosen diagonal. Let's say this midpoint is M.
3. Connect the midpoint to opposite vertices: Draw two lines connecting the midpoint, M, to the opposite vertices of the rectangle. In this case, connect M to vertices A and C.
4. Measure the distance: Using a ruler or any other measuring tool, measure the length from the midpoint, M, to any of the vertices, such as A. This distance will be the radius of the circle we want to draw.
5. Draw the circle: With the measured radius, place the tip of your compass or any circular object with the measured radius on the midpoint, M. Then, rotate the compass or circular object around M to draw the circle. The circle should pass through all four vertices of the rectangle.
By following these steps, you will be able to draw a circle that passes through all the vertices of a rectangle. Keep in mind that this method works because a rectangle has special properties, such as diagonals that bisect each other and are congruent.