Read more about this in our circumference calculator and arc length calculator. Lets take a look at a few problems involving central angles and chords. The same method may be used to find arc length – all you need to remember is the formula for a circle's circumference. So, what's the area for the sector of a circle:įrom the proportion, we can easily find the final sector area formula: Then, we want to calculate the area of a part of a circle, expressed by the central angle.įor angles of 2π (full circle), the area is equal to πr²: The full angle is 2π in radians, or 360° in degrees, the latter of which is the more common angle unit. The area of a circle is calculated as A = πr². For example, if you have two points on a circle, A, and B, then the perpendicular bisector of their chord (the line segment AB) will pass through the midpoint of AB and intersect the circle at right. All you need to remember is the circle area formula (and we bet you do!): A perpendicular bisector of a chord is a line that passes through the midpoint of two points on a curve and intersects the curve at right angles. Retrieved – via Canadian Center of Science and Education.The formula for sector area is simple – multiply the central angle by the radius squared, and divide by 2:īut where does it come from? You can find it by using proportions. "On the hidden beauty of trigonometric functions". On the Shoulders of Giants: The Great Works of Physics and Astronomy. Greenbelt, Maryland, US: NASA Goddard Space Flight Center.
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