Perpendicular Bisector
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Definition of Perpendicular Bisector
Perpendicular Bisector is a perpendicular line or a segment that passes through the midpoint of a line.
More About Perpendicular Bisector
 A perpendicular bisector divides a line segment into two equal segments.
 The intersecting point of the three perpendicular bisectors of a triangle is called circumcenter.
Examples of Perpendicular Bisector

In the figure shown, AB is the perpendicular bisector of the line segment PQ passing
through its midpoint 'O'.
Video Examples: Perpendicular Bisector of a Triangle  MathHelp.com
Solved Example on Perpendicular Bisector
Ques: AB is a line segment of length 12 cm. CD is the perpendicular bisector of AB. Find the length of AO and OB.
Choices:
A. 6 cm and 8 cmB. 7 cm and 7 cm
C. 6 cm and 6 cm
D. 7 cm and 6 cm
Correct Answer: C
Solution:

Step 1: A perpendicular bisector divides a line segment into two equal parts.
Step 2: The length of AB is 12 cm and CD is the perpendicular bisector of AB.
Step 3: So, AO = OB = = = 6 [Substitute AB = 12.]
Step 4: AO = OB = 6 cm
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