document.write( "Question 1061271: In any triangle ABC, E is any point on altitude line segment AD. Prove that (AC)^2-(CE)^2= (AB)^2-(EB)^2 \n" ); document.write( "

Algebra.Com's Answer #676190 by ikleyn(52835) $\"\"$ $\"About$

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\n" ); document.write( "In any triangle ABC, E is any point on altitude line segment AD. Prove that (AC)^2-(CE)^2= (AB)^2-(EB)^2
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document.write( "0.  Make a sketch to follow my arguments.\r\n" );
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document.write( "1.  From the triangle ADC:   = .\r\n" );
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document.write( "    From the triangle EDC:   = .\r\n" );
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document.write( "    It implies   = .\r\n" );
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document.write( "    Hence,       = .   (1)\r\n" );
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document.write( "2.  Similarly,\r\n" );
document.write( "    From the triangle ADB:   = .\r\n" );
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document.write( "    From the triangle EDC:   = .\r\n" );
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document.write( "    It implies   = .\r\n" );
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document.write( "    Hence,       = .   (2)\r\n" );
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document.write( "3.  From (1) and (2) you have \r\n" );
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document.write( "     = .\r\n" );
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document.write( "It is what has to be proved.\r\n" );
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