Circles

 

A circle is a geometrical figure that always confuses all aspirants of the GRE Test since many geometrical figures combined with circles makes it complex.

A circle is a collection of points that are present at equal distances from a common point which is known as the center of the circle. The equidistant length between the center and the collection of points is known as the radius.

And if a line is drawn connecting two points of circle, passing through center then it is known as diameter of the circle. Alternatively, twice of radius is equal to the diameter.

Last comes the circumference of the circle and can be calculated as pi times diameter (pi*d) or pi times twice of radius (2*pi*r). The universal value defined for pi is 22/7 or approximately 3.14. Commonly, the designated letter used for representing a circle and attributed to its center point is either O, A or C.

Center, Radius, Diameter
Let us look at a few definitions associated with the circle.

Arc: It is a curved line which is a part of the circumference of the circle.

Arc
Sector: It is like a slice of cake (a circle wedge)

Sector
Chord: It is a line segment inside the circle that touches 2 points on the circumference of the circle. The largest possible chord within a circle is the diameter.

Chord
Tangent of the circle: It is a line perpendicular to the radius which touches the circle at one and ONLY one point

Tangent
Area of Circle=A=πr2

Area of Circle=A=πr2 OR π(d/2)2

Arc Length: The length of the circular arc if the central angle is equal to Θ

If Θ is in radians then arc length = Θ×r

But, if Θ is in degree then arc length = Θ/360°×2π*r

Area of sector if the central angle is Θ

If the angle is in radians then area of sector = Θ/2*r2

If the angle is in degree then area of sector = πr2×Θ /360°

Thus we hope these formulas assist to tackle this section of the GRE syllabus for quantitative reasoning.

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