Thursday, 13 July 2017

Circle II - 5 Important Circle Formulas To Solve Circle Questions On Chord Length

In this post, we have discussed Important Circle Formulas that will help you solve Circle Questions on Chord Lengths and help you save time in SSC Exams
Circle Formulas, Circle Questions, Chord Length

It is difficult to remember circle formulas to solve circle questions that ask you to calculate Chord Length in SSC Exams. In this post, we have listed all chord properties and circle formulas that will help you calculate chord length easily. 

This is the second post in the series of circles. In the first post, what is a circle? – Definitions, Formulae and different parts of a circle, we have discussed different parts, properties, formulas and definitions of circles that will help you learn the list of circle formulas to measure chord length within few minutes.
Circle Formulas, Circle Questions, Chord Length

What is a chord?

A chord is a straight line joining any two points on the circumference of the circle.


Circle Formulas, Circle Questions, Chord Length


List of Circle Formulas to Calculate Chord Length


Circle Formula 1: When a perpendicular is drawn from the centre of the circle to the chord, it bisects the chord into two equal halves.

Let's say that AB is a chord. If a line is drawn from the centre of the circle O till the chord AB, then this line will bisect the chord in into two equal halves. 

Circle Formulas, Circle Questions, Chord Length


Circle Formula 2: Two chords that are equal in length are always equidistant from the centre of the circle.

Let's say that AB and A'B' are two chords in a circle of equal length, then AB and A'B' will be equidistant from the centre O.

Circle Formulas, Circle Questions, Chord Length

Circle Formulas, Circle Questions, Chord Length


Circle Formula 3: If two chords AB and CD intersects at a point E internally or externally then,
AE x EB = CE x ED

Circle Formulas, Circle Questions, Chord Length


Circle Formulas, Circle Questions, Chord Length


Circle Formula 4: The two circles intersect each other, then they intersect at two points. hence, when we join the two points and we get a chord which is common for both the circles.

Property:
Common chord is perpendicular to the line joining the centre irrespective of the size of the circle or length of the radius.


Circle Formulas, Circle Questions, Chord Length


Circle Formula 5: Angle subtended by (minor arc/major arc) at the centre is twice the angle subtended at any point on the (major arc/minor arc)


Circle Formulas, Circle Questions, Chord Length


Circle Formulas, Circle Questions, Chord Length

Circle Formulas, Circle Questions, Chord Length

The angle subtended at the centre of a circle is twice the angle subtended by any arc of the other side of a circle.( Semi Circle)


Circle Formulas, Circle Questions, Chord Length

Hope these have been of help to you while preparing for SSC CGL 2017 as questions on Circles are a common occurrence in these competitive exams. 

Do write in the comment section below on how these circle formulas have helped you solve circle questions asked in mock tests for SSC CGL on finding chord length of given chord in a circle. Also, download free questionnaire for practice!

Stay tuned for our next blog in the same series on tangents.
Circle Formulas, Circle Questions, Chord Length
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