document.write( "Question 1102480: In △ABC, m∠CAB = 60° and point D ∈ BC so that AD = 10 in, and the distance from D to AB is 5in. Prove that AD is the angle bisector of ∠A. \n" ); document.write( "

Algebra.Com's Answer #717190 by ikleyn(52847) $\"\"$ $\"About$

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\n" ); document.write( "In △ABC, m∠CAB = 60° and point D ∈ BC so that AD = 10 in, and the distance from D to AB is 5 in.
\n" ); document.write( "Prove that AD is the angle bisector of ∠A.
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document.write( "0.  Make a sketch to follow my proof.\r\n" );
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document.write( "1.  The fact that \"the distance from D to AB is 5 in\" means \r\n" );
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document.write( "    that the length of the perpendicular drawn from the point D to the side AB is 5 inches.\r\n" );
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document.write( "    Draw this perpendicular. Let E be the intersection point of this perpendicular with the side AB.\r\n" );
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document.write( "    You have a right-angled triangle ADE.  Its hypotenuse AD is 10 in long.\r\n" );
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document.write( "    Its leg DE is 5 inches long.\r\n" );
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document.write( "    Hence, the angle EAD is 30°.\r\n" );
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document.write( "    The measure of the angle EAD is the same as the measure of the angle BAD.\r\n" );
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document.write( "    It implies that AD is the angle bisector of the angle BAC.\r\n" );
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\n" ); document.write( "\n" ); document.write( "QED.\r
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