   Question Answers

# AB and CD are the two common tangent to circles which touch each other at C. If D lies on AB such that CD = 4 cm, then AB is equal to A.4 cm B.6 cm C.8 cm D.12 cm  Hint: Before attempting this question remember to construct the diagram using the given information and use Point C is the common point that lie on the circumference of both the circles, use this information to approach towards the solution of the given question

Let’s construct the diagram using the given information
According to the given information we have two circles which touch each other at point C also the circle have 2 common tangents AB and CD
And there is a point D which lie on AB such that CD = 4cm
So the constructed diagram is To find the value of AB let join Point B and C and point A and C so the diagram we get is As we know that the two tangent drawn from the same external point from the circle are equal in length
Therefore we can say that CD = DB
Since CD = DB so DB = 4 cm
Similarly for tangent AD and DC by the property of tangent from the same external point form circle
Since AB is equal to AD + DB i.e. AB = AD + DB
Substituting the given values in the above equation we get
AB = 4 cm + 4 cm
AB = 8 cm
Since the measure of AB is 8 cm.
So, the correct answer is “Option C”.

Note: The concept of tangent played a main role to solve the above problem which can be explained as the line which intersect circle at one point that lie on the circumference of the circle here at the point where tangent intersect the circle, radius of the circle becomes perpendicular to the tangent. There are some basic properties that are shown by the tangent such as: the line of tangent never passes through the circle and the tangent drawn from the external points of the circle are equal to each other.
Tangent Formula  To Determine the Mass of Two Different Objects Using a Beam Balance  What are the Successor and Predecessor?  CBSE Class 10 Maths Chapter 10 - Circles Formula  What are the Functions of the Human Skeletal System?  CBSE Class 9 Maths Chapter 6 - Lines and Angles Formulas  Common Cold  CBSE Class 9 Maths Chapter 13 - Surface Areas and Volumes Formulas  CBSE Class 10 Maths Chapter 8 - Introduction to Trigonometry Formula  CBSE Class 8 Maths Chapter 15 - Introduction to Graphs Formulas  Important Questions for CBSE Class 10 Maths Chapter 12 - Areas Related to Circles  Important Questions for CBSE Class 9 Maths Chapter 10 - Circles  Important Questions for CBSE Class 6 English A Pact with The Sun Chapter 9 - What Happened to The Reptiles  Important Questions for CBSE Class 9 Maths Chapter 5 - Introduction to Euclids Geometry  Important Questions for CBSE Class 9 Maths Chapter 4 - Linear Equations in Two Variables  Important Questions for CBSE Class 6 English A Pact with The Sun Chapter 1 - A Tale of Two Birds  Important Questions for CBSE Class 9 Maths Chapter 9 - Areas of Parallelograms and Triangles  CBSE Class 7 Science Fibre to Fabric Worksheets  CBSE Class 6 Science Fibre to Fabric Worksheets  Important Questions for CBSE Class 10 Maths Chapter 10 - Circles  CBSE Class 12 Maths Question Paper 2020  CBSE Class 10 Hindi A Question Paper 2020  Hindi A Class 10 CBSE Question Paper 2009  Hindi A Class 10 CBSE Question Paper 2015  Hindi A Class 10 CBSE Question Paper 2007  Hindi A Class 10 CBSE Question Paper 2013  CBSE Class 10 Maths Question Paper 2020  CBSE Class 10 Maths Question Paper 2017  Hindi A Class 10 CBSE Question Paper 2016  Hindi A Class 10 CBSE Question Paper 2012  RD Sharma Solutions for Class 9 Maths Chapter 16 - Circles  NCERT Solutions for Class 9 Maths Chapter 10 Circles  NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles  RD Sharma Solutions for Class 10 Maths Chapter 15 - Areas Related to Circles  NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry  RD Sharma Solutions for Class 9 Maths Chapter 7 - Introduction to Euclid's Geometry  NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles in Hindi  NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables  NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles  NCERT Exemplar for Class 10 Maths Chapter 11 - Areas Related to Circles (Book Solutions)  