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Maths-

General

Easy

Question

In △ABC, AD⊥BC Also, $B D equals 3 C D$ Prove that $2 A B squared equals 2 A C squared plus B C squared$

hint Hint:

using pythagoras theorem Find $AC squared$ and $AB squared$ subtract both the equation and substitute given conditions

The correct answer is: Hence proved

Aim :- Prove that $2 AB squared equals 2 AC squared plus BC squared$
As BD = 3 CD ;We get BC = BD +CD = 4 CD
Applying pythagoras theorem in ΔACD ,We get
$AC squared equals AD squared plus CD squared$

Applying pythagoras theorem in ΔABD ,We get
$AB squared equals BD squared plus AD squared not stretchy rightwards double arrow AD squared equals AB squared minus BD squared$ —Eq2
Substitute Eq2 in Eq1 ,
$AC squared equals AB squared minus BD squared plus CD squared not stretchy rightwards double arrow AC squared equals AB squared plus CD squared minus BD squared$
As BD = 3 CD ;We get $A C squared equals A B squared plus C D squared minus 9 C D squared$
$AC squared equals AB squared minus 8 CD squared not stretchy rightwards double arrow 8 CD squared plus AC squared equals AB squared$
Multiplying with 2 on both sides
$left parenthesis 4 CD right parenthesis squared plus 2 AC squared equals 2 AB squared$ As BC = 4 CD
∴ $2 AB squared equals 2 AC squared plus BC squared$
Hence proved

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