Introduction: The Diameter Puzzle
So, once again, a Puzzle. Simplest of its kind. I remember it from a time when I was organizing a Mathematics Competition at my school. And yes, this was a question in it.
I hope you enjoy it as much I did once.
Step 1: The Puzzle
You are given a circle card, a rectangle card, and a pencil. Using only the three objects,and without folding or tampering them, mark the diametric line on the circle.
Step 2: The Property
Simply put: the chord that makes a right angle at the circumference of a circle is the diameter.
Any angle made at the circumference by the diametric line will be 90°.
Step 3: How to Do It?
Put one corner of the rectangle on the circumference and make lines with the aid of the edges on either side. Now join the two points, where the lines again meet the circumference, to make a line with your pencil. That's your diameter! Simple.
As each vertex of a rectangle is a right angle, the angle made at the circumference is a right angle. Following this, the line that makes it turns out to be the diameter.