Geometry and the Circle (Part 1)

A circle is an important shape in the field of geometry. Let's look at the definition of a circle and its parts. We will also examine the relationship between the circle and the plane.

A circle is a shape with all points the same distance from its center. A circle is named by its center. Thus, the circle to the right is called circle A since its center is at point A. Some real world examples of a circle are a wheel, a dinner plate and (the surface of) a coin.
The distance across a circle through the center is called the diameter. A real-world example of diameter is a 9-inch plate.
The radius of a circle is the distance from the center of a circle to any point on the circle. If you place two radii end-to-end in a circle, you would have the same length as one diameter. Thus, the diameter of a circle is twice as long as the radius.
We can look at a pizza pie to find real-world examples of diameter and radius. Look at the pizza to the right which has been sliced into 8 equal parts through its center. A radius is formed by making a straight cut from the center to a point on the circle. A straight cut made from a point on the circle, continuing through its center to another point on the circle, is a diameter. As you can see, a circle has many different radii and diameters, each passing through its center.
A chord is a line segment that joins two points on a curve. In geometry, a chord is often used to describe a line segment joining two endpoints that lie on a circle. The circle to the right contains chord AB. If this circle was a pizza pie, you could cut off a piece of pizza along chord AB. By cutting along chord AB, you are cutting off a segment of pizza that includes this chord.
A circle has many different chords. Some chords pass through the center and some do not. A chord that passes through the center is called a diameter.
It turns out that a diameter of a circle is the longest chord of that circle since it passes through the center. A diameter satisfies the definition of a chord, however, a chord is not necessarily a diameter. This is because every diameter passes through the center of a circle, but some chords do not pass through the center. Thus, it can be stated, every diameter is a chord, but not every chord is a diameter.
Let's revisit the definition of a circle. A circle is the set of points that are equidistant from a special point in the plane. The special point is the center. In the circle to the right, the center is point A. Thus we have circle A.
A plane is a flat surface that extends without end in all directions. In the diagram to the right, Plane P contains points A, B and C.
Can you think of some real world objects that satisfy the definition of a plane? At this level of mathematics, that is difficult to do. Intuitively, a plane may be visualized as a flat infinite sheet of paper. The top of your desk and a chalkboard are objects which can be used to represent a plane, although they do not satisfy the definition above.

A circle divides the plane into three parts: the points INSIDE the circle the points OUTSIDE the circle and the points ON the circle

the points inside the circle	the points outside the circle	the points on the circle

You can see an interactive demonstration of this by placing your mouse over the three items below.
A circle divides a plane into three parts: the points INSIDE the circle  the points OUTSIDE the circle  and the points ON the circle

Unpaid salaries: Students hold Osun dep gov hostage

Students of tertiary institutions owned by Osun State Government on Monday staged a massive protest in Osogbo against the prolonged strike by their lecturers. The lecturers in four state-owened institutions embarked on an indefinite strike over three months ago as a result of unpaid salaries, inadequate staff and non remittance of their pension deduction made by the state government to the retirement savings accounts. The students, mostly from Osun State Polytechnic, Iree; Osun State College of Technology, Esa Oke; Colleges of Education in Ila and Ilesa, started the protest from Olaiya and trekked to Abere, the State Secretariat singing anti-government songs. The students had laid siege to the main gate of the state secretariat after they arrived there at around 11am. At around 12:50pm, the Deputy Governor, Mrs. Titi Laoye-Tomori, was driven to the secretariat but the students prevented her convoy from gaining entry. Some of the students laid on the ground in front of her car and some laid at the back making it difficult for the deputy to go inside or to turn back. All efforts made by Laoye-Tomori to pacify the irate students failed as they held her hostage in their midst. Some of the students had earlier manhandled the Permanent Secretary, Ministry of Education, Mr. Lawrence Oyeniran, by poking his stomach and making jest of him. The Chairman, National Association of Nigerian Students, Osun State, Mr. Lukman Adekitan, said the students were tired of staying at home due to the strike in the four institutions. He called on Governor Rauf Aregbesola to addressed the issues raised by the lecturers, saying students of the affected schools have wasted a lot of time due to incessant strikes.