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Results Deduced From Pythagoras Theorem

Triangles II - Concepts

Calculating Perimeter of Triangle

Area of Similar Triangles

Similarity Related To Right Triangle

Pythagoras Theorem

Results Deduced From Pythagoras Theorem

Class - 10th IMO Subjects

Concept Explanation

Results Deduced From Pythagoras Theorem

Result 1 : In the given $large Delta$ ABC, obtuse angled at B if AD $large perp$ CB produced, then $large AC^2= AB^2 +BC^2+2BC. BD$

Given: $large Delta$ ABC obtuse angled at B if AD $large perp$ CB produced,

To Prove: $large AC^2= AB^2 +BC^2+2BC. BD$

Proof:

In $large Delta ADB$ right angled at D

$large AB^2= AD^2+BD^2$ [ By Pythagoras Theorem ] .........(1)

In $large Delta ADC$ right angled at D

$large AC^2= AD^2+CD^2$ [ By Pythagoras Theorem ]

$large AC^2= AD^2+(BD + BC) ^2$

$large AC^2= AD^2+BD^2 + BC^2+ 2 BD.BC$

$large AC^2= (AD^2+BD^2 )+ BC^2+ 2 BD.BC$

$large AC^2= AB^2 + BC^2+ 2 BD.BC$ [From Equation 1]

Result 2 : In the given $large Delta$ ABC, if angle B is an acute angle and AD $large perp$ BC, then $large large AC^2= AB^2 +BC^2-2BC. BD$

Given: In $large Delta$ ABC angle B is an acute angle and AD $large perp$ BC,

To Prove: $large AC^2= AB^2 +BC^2-2BC. BD$

Proof: In $large Delta ADB$ right angled at D

$large AB^2= AD^2+BD^2$ [ By Pythagoras Theorem ] .........(1)

In $large Delta ADC$ right angled at D

$large AC^2= AD^2+CD^2$ [ By Pythagoras Theorem ]

$large AC^2= AD^2+(BC -BD) ^2$

$large AC^2= AD^2+BD^2 + BC^2 - 2 BD.BC$

$large AC^2= (AD^2+BD^2 )+ BC^2 - 2 BD.BC$

$large AC^2= AB^2 + BC^2 - 2 BD.BC$ From Equation (1)

Sample Questions

(More Questions for each concept available in Login)

Question : 1

If is such that $angle B=120^{0}$ and and AC = 12 cm, AB = 3 cm, BD = 2 cm. Then Find BC.
A. $-2-sqrt{139}$	B. $-2+sqrt{139}$	C. $-2pm sqrt{139}$	D. none of these
Right Option : B
View Explanation

Question : 2

If $bigtriangleup ABC$ is such that $angle B=30^{0}$ and and AB = 13 cm, BC = 7 cm, BD = 5 cm. Then Find AC.
A. $sqrt{288}$	B. $sqrt{158}$	C. $sqrt{278}$	D. $sqrt{148}$
Right Option : D
View Explanation

Question : 3

If $bigtriangleup ABC$ is such that $angle B=120^{0}$ and $ADperp CB$ and AB = 5 cm, BC = 4 cm, BD = 2 cm. Then Find AC.
A. $sqrt{53}$		B. $sqrt{57}$
C. $sqrt{47}$		D. $sqrt{43}$
Right Option : B
View Explanation

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Chapters

Real Numbers I

Real Numbers II

Pair of Linear Equations I

Pair of Linear Equations II

Polynomial I

Polynomials II

Quadratic Equations I

Quadratic Equations II

Introduction to Trigonometry I

Introduction to Trigonometry II

Arithmetic Progression I

Arithmetic Progression II

Triangles I

Triangles II

Some Applications of Trigonometry

Coordinate Geometry I

Coordinate Geometry II

Introduction to Trigonometry

Direct and Inverse Variation

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Areas Related to Circles

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Attention !!!!!

Results Deduced From Pythagoras Theorem

Results Deduced From Pythagoras Theorem

Students / Parents Reviews [10]

Manish Kumar

Yatharthi Sharma

Barkha Arora

Aman Kumar Shrivastava

Prisha Gupta

Ayan Ghosh

Archit Segal

Om Umang

Cheshta

Shreya Shrivastava