Friday, 14 July 2017

Circles III - The A- Z of Tangent Formula to Solve Circle Questions

In this post, we will discuss all the tangent formulas that will help you solve circle questions and save time in SSC CGL Exam.

Tangent Formula

Questions from geometry section, especially circle questions always appear in SSC Exams. These Circle Questions can be easily solved with the help of formulas. 

This is the third post in the series of Circles. In this post, we will discuss tangent formulas that will help you solve circle questions easily and thus help you save time during SSC Exams. 

Before moving further, let’s quickly review the concept of circles. 
Tangent Formula

What Is A Tangent?

A tangent is a line that touches the circle exactly at one point on the circumference of a circle. 

Tangent Formula

What Is A Secant?

Secant is a line that touches the circumference or cuts the circumference of the circle at two points. 

Tangent Formula

List of Tangent Formulas to Solve Circle Questions 

Tangent Formula 1: 

The angle between the tangent and the radius of the circle at the point of contact is 90 degrees. 

Tangent Formula

Tangent Formula 2: 

This property is based on the Length of a tangent: 

1. The length of two tangents from an external point is equal in length. 

Tangent Formula

2. Tangent Formula to measure the length of a chord

Let's take the distance between the centre and the point P as ‘d’ At the point of contact, where the radius and tangent meet  90 degree - right angle is formed. Now we get two right angled triangles. 

OAP and OBP are right angled triangles. Hence, by using Pythagoras theorem, we know that OA is the radius, OP is the distance and  AP is the hypotenuse. Therefore, hypotenuse AP which is the tangent can be found by:

√d² - r²

Tangent Formula

Tangent Formula 3: 

This tangent formula is based on a tangent and a secant. 

1.There is a circle, from external point P we draw a tangent and a secant.
PT is the length of the tangents and TBA is the length of the secant. Therefore,

PT² = PA x PB

Hence, When we draw a tangent and secant from an external point then, the length of the tangent square will be equal to PA and PB 

2. When we draw two secant lines, suppose PAB and PCD then,

 PA x PB = PC x PD 

Tangent Formula

Have a look at chord formulas too, to have a firm grip over circle questions. 

Tangent Formula

Hope these tangent formulas 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 Tangent Formulas 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 tangents.
Tangent Formula

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