Monday, 17 July 2017

Circle IV – How to Learn Circle Formulas for Intersecting Circles

In this post, we will discuss Circle Formulas for Intersecting Circles that will help you solve circle questions in SSC CGL Exams

intersecting circles

Geometry is a vast subject. It is a subject related to shape, size, properties etc. Though it’s a part of mathematics, it is a completely different sector.  Anything from geometry can be asked in SSC CGL or any other competitive exam. In this post, we have discussed few Circle Formulas for intersecting circles that will help you solve Circle questions in less time. Thus, helping you save time in SSC Exams.

In our previous posts, we have discussed concepts such as – Circles, Important chord formulas and Tangent Formulas. Hence, before moving further, let us recap these concept of Circles. 
intersecting circles

Intersecting Circles: 

Intersecting circles are those circles which touch each other at a point. 


A pair of Intersecting Circles: 

When there are two circles irrespective of their sizes touch each other externally, the point at which they contact is colonial to the centre of both circles. This means that all the three points i.e. centre of circle O, the colonial point P and the centre of circle Oٰ lie on the straight line.
intersecting circles


Pair of Intersecting Circles which do not touch each other 

When we have non-intersecting circles then that pair of circles will have two types of tangents. 

1. Common Tangent: There can be only two common tangents in a pair of circles. 
Common tangents are straight in nature. 


AB and A'B' are common tangents

intersecting circles


2. Transverse Tangent (Cross Tangent): There can be only two transverse tangents in a pair of circles. Transverse tangents are cross in nature. 


AB and CD are two transverse tangents
intersecting circles
intersecting circles

How to measure the length of the tangents of two non-intersecting circles

Let us assume the distance between the two centres of circles to be “d”
Let us assume the radius of circle O as “r”
Let us assume the radius of circle O¹ as “r¹”
Then, 
intersecting circles

intersecting circles

intersecting circles


How to measure the length of the tangents of two intersecting circles

When there are two intersecting circles then there will be only two direct tangents that can be drawn. 
intersecting circles


intersecting circles

How to measure the length of the tangents of two internally intersecting circles 

When two circles intersect each other internally then we can draw only one transverse or common tangent.

Here, distance between the two centres can be calculated as  
intersecting circles

How to measure the length of the tangents of two Circles which have common centres

When two circles share common centres then we cannot draw any tangent.


intersecting circles

Hope these circles formulas on intersecting circles have been of help to you while preparing for SSC CGL 2017 as circle questions often appear in these competitive exams. 

Do write in the comment section below on how these circle formulas on intersecting circles have helped you solve circle questions asked in mock tests for SSC CGL. Also, download free questionnaire for practice!

Stay tuned for our next blog in the same series on Cyclic Quadrilateral. 
intersecting circles
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