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Maths-

General

Easy

Question

In Triangle $A B C comma straight angle A D B equals 90 to the power of ring operator$ . Prove that $A B squared equals A C squared plus B C squared minus 2 B C times C D$

hint Hint:

Hint :- Applying pythagoras theorem to both triangles ABD and ADC. find the AD2 from both equations .Equate both the equations to get the required condition .

The correct answer is: Hence proved

Aim :- Prove that   $A B squared equals A C squared plus B C squared minus 2 B C times C D$
Explanation(proof ) :-Applying pythagoras theorem in Δ ACD ,We get
$A C squared equals A D squared plus C D squared$ — Eq1
Applying pythagoras theorem in Δ ABD ,We get
$A B squared equals B D squared plus A D squared not stretchy rightwards double arrow A D squared equals A B squared minus B D squared minus Eq 2$
Substitute Eq1 in Eq2 ,
$A C squared equals A B squared minus B D squared plus C D squared not stretchy rightwards double arrow A C squared equals A B squared plus C D squared minus B D squared$
$text By using end text a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis text and end text B C equals B D plus C D text we get, end text$
   $not stretchy rightwards double arrow A C squared equals A B squared plus left parenthesis B D plus C D right parenthesis left parenthesis C D minus B D right parenthesis$
$not stretchy rightwards double arrow A C squared equals A B squared plus B C left parenthesis 2 C D minus B C right parenthesis$
   $A C squared equals A B squared plus 2 B C. C D minus B C squared$
$A C squared plus B C squared minus 2 B C times C D equals A B squared$
$therefore space A B squared equals A C squared plus B C squared minus 2 B C times C D$
Hence proved

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