In the GMAT, circles and its properties is a common question that is asked in the quantitative section. These are just basic Geometry questions that you must have learnt in high-school. Hence, all you need to do is brush up on this topic well, take up some sample questions and practice as much as you can. If you are fresh out of college, revising this topic wouldn’t take you much time but if you are a professional who hasn’t stayed in touch with Geometry for a long time, then you might need to pay extra attention. However, once you learn the concepts and formulas and practice questions well enough, then you can surely solve these problems with ease.
In this article, we will cover some basic concepts of the circle, we will talk about circle properties and also provide some important formulas for you to memorize.
Circle: Basic Concepts
Before we move onto the properties of a circle, let’s understand the basic circle concepts.
- Radius: The radius refers to a distance between the center and any point on the boundary of the circle. It is identified by the letter “R”.
- Diameter: The diameter refers to a distance between any two points on the boundary of the circle. It runs across the circle as a line and is identified by the letter “D”. The diameter, when broken down into two parts, becomes two radii. Hence, D= 2R
- Center: The fixed middle point of the circle is the center.
- Semi- circle: When the circle is divided into two equal parts, it is referred to as the semi-circle.
- Circumference: The circumference refers to the area that boundaries the circle.
- Arc: The arc of the circle refers to any two pints on the circumference. There are two kinds of arcs— minor and major arcs. If the distance between two points is shorter, then it becomes a minor arc and the remaining arc of the circle is the major arc.
- Sector: When the two ends of arc meet at the center of the circle, the area within is known as a sector. Yet again, there are two kinds of sectors— major and minor sectors.
The properties of a circle are as follows:
- Chord: A chord refers to a line, wherein each end lies on the boundary of the circle. The property of the chord is such that a perpendicular drawn from the center, divides any chord into two equal parts.
- Tangent: A tangent refers to a line that connects any point of the circle at its boundary. The property of the tangent is such that the radius is always perpendicular to the tangent.
- Inscribed angle: When two chords meet at the center of the circle and the other end of each of the chords lie on the boundary of a circle, the area within it forms the inscribed angle. The property of an inscribed angle is such that if there are two arcs on the circumference of the circle, the inscribed angles of both the arcs are equal.
- Semi-circle: The angle of the semi-circle is always 90 degrees.
- Central angle: When two lines join at the center and the other ends lies on the boundary of the circle, the angle of the area within refers to the central angle. The property of the central angle is such that if the central angle and the inscribed angle are on the same arc, then the central angle is always twice of the inscribed angle.
- Area of circle — The area of the circle is measured by the formula— 𝜋 x R.
- Perimeter — The perimeter of the circle is measured by the formula— 2x 𝜋x R
Circle and its properties as mentioned before is an important part of the quant section, hence, makes sure you learn the basic concepts and formulas. Doing so will make solving circle questions easier.