RS Aggarwal Class 10 Solutions

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RS Aggarwal Class 10 Solutions
RS Aggarwal Class 10 Solutions
NCERT Solutions for Class 10 Maths Chapter 10 Circles
This content is part of NCERT Solutions for Class 10 Maths Chapter 10 Circles
9.4 THEORM :
Statement : Lengths of two tangents drawn from an external point to a circle are equal.
Given: AP and AQ are two tangents drawn from a point A to a circle C (O, r).
To prove : AP = AQ
Construction : Join OP, OQ and OA.
Proof : In AOQ and APO
[Tangent at any point of a circle is perp. to radius through the point of contact]
AO = AO [Common]
OQ = OP [Radius]
So, by R.H.S. criterion of congruency
AQ = AP [By CPCT] Hence Proved.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles: THALES THEOREM
This content is part of NCERT Solutions for Class 10 Maths Chapter 6 Triangles
THALES THEOREM (BASIC PROPROTIONALITY THEOREM) :
Statement : If a line is drawn parallel to one side of a triangle to intersect the other sides in distinct points, then the other two sides are divided in the same ratio.
Given: A triangle ABC in which a line parallel to side
BC intersects other two sides AB and AC at D and
E respectively.
To Prove :
Construction : Join BE and CD and draw DMAC and ENAB.
Proof : Area of DADE (=base × height) = AD × EN.
Area of DADE is denoted as are (ADE)
So, ar(ADE) = DB × EN
And ar(BDE) = DB × EN ,
Therefore, ….(i)
Similarly, ar(ADE =AE × DM and ar(DEC =EC × DM.
And ......(ii)
Note that D BDE and D DEC are on the same base DE and between the two parallel lines BC and DE.
So, ar(BDE) = ar(DEC) .....(iii)
Therefore, from (i), (ii) and (iii), we have :
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RD-Sharma-class 10-maths-Solutions-chapter 15-Areas related to Circles- Exercise 15.1-Question-10_1 #RDSharmaClass10 #Class10Solutions #RDSharmaClass10Solutions #AreasRelatedCircles #RDSharma #LearnCBSE
RD-Sharma-class 10-maths-Solutions-chapter 15-Areas related to Circles- Exercise 15.1-Question-6 #RDSharmaClass10 #Class10Solutions #RDSharmaClass10Solutions #AreasRelatedCircles #RDSharma #LearnCBSE
RD-Sharma-class 10-maths-Solutions-chapter 15-Areas related to Circles- Exercise 15.3-Question-3 #RDSharmaClass10 #Class10Solutions #RDSharmaClass10Solutions #AreasRelatedCircles #RDSharma #LearnCBSE
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Northern California ‘Forest House’
© Richard Barnes
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