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Example: Construct Perpendicular Bisector of Chords

 Post to:   Explanation:

Circle Circle illustration showing a radius, a diameter, the centre and the circumference

A circle is a simple shape of Euclidean geometry consisting of the set of points in a plane that is a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius.

Circles are simple closed curves which divide the plane into two regions: an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure, or to the whole figure including its interior; in strict technical usage, the circle is the former and the latter is called a disk.

A chord is a line segment whose endpoints lie on the circle. (Our solved example in mathguru.com uses this concept)

A diameter is the longest chord in a circle.

http://en.wikipedia.org/wiki/Circle

# Bisection

In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector. The most often considered types of bisectors are the segment bisector (a line that passes through the midpoint of a given segment) and the angle bisector (a line that passes through the apex of an angle that divides it into two equal angles).

## Line segment bisector

A line segment bisector passes through the midpoint of the segment. Particularly important is the perpendicular bisector of a segment, which, according to its name, meets the segment at right angles. The perpendicular bisector of a segment also has the property that each of its points is equidistant from the segment's endpoints. (Our solved example in mathguru.com uses this concept)

http://en.wikipedia.org/wiki/Bisection

(Our solved example in mathguru.com also uses the below concept. This is our own explanation, it is not taken from Wikipedia.)

Steps of Construction to draw perpendicular bisector of any line segment AB (say)

1.       Taking A as centre and radius more than half of AB, draw an arc above and below AB

2.       Similarly, from B with the same radius draw another arc intersecting previous arcs

3.       Join the two points