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Maths-

General

Easy

Question

$text In a right angled Triangle end text A B C comma less than B equals 90 to the power of ring operator text and end text D text is the mid point of end text B C text . Prove that end text A C squared equals A D squared plus 3 C D$

hint Hint:

Hint :- use pythagoras theorem in triangle ABD and ABC
We get AC2 and AD2 subtract them and substitute BC = 2BD
In the equation to get the result.

The correct answer is: Hence proved

Aim :- Prove that $A C squared equals A D squared plus 3 C D squared$
Explanation(proof ) :-
Applying pythagoras theorem in triangle ABC,we get
$A C squared equals A B squared plus B C squared$ —- Eq1
Applying pythagoras theorem in triangle ABD ,we get
$A D squared equals A B squared plus B D squared$ — Eq2
As AD is median , D is mid point then BC = 2BD

Subtract Eq1 - Eq2
We get , $A C squared minus A D squared equals A B squared plus B C squared minus open parentheses A B squared plus B D squared close parentheses$
$A C squared minus A D squared equals B C squared minus B D squared text substitute end text BC equals 2 BD$
$A C squared minus A D squared equals 4 B D squared minus B D squared$
As D is mid point BD = CD ,
substitute BD = CD in the above equation
$A C squared minus A D squared equals 3 C D squared$
∴ $A C squared equals A D squared plus 3 C D squared$
Hence proved

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