document.write( "Question 1150801: If the lengths of the bases of an isosceles trapezoid inscribed in a circle are 10 cm and 22 cm, and if one of the legs is 10 cm, then what is the length of a diagonal, in cm? \n" ); document.write( "

Algebra.Com's Answer #772260 by MathLover1(20850) $\"\"$ $\"About$

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document.write( "Make a sketch.\r\n" );
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document.write( "Let ABCD be the given isosceles trapezoid.\r\n" );
document.write( "The bases are AB = 22 cm long;  CD = 10 cm;\r\n" );
document.write( "the lateral sides are AD = BC = 10 cm.\r\n" );
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document.write( "Draw the perpendiculars CE and DF from the vertices C  and D to the base AB.\r\n" );
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document.write( "It is clear that the right-angled triangles ADF  and BCE are congruent.\r\n" );
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document.write( "Then the segments AF and BE have the length   =  =  = 6 cm each.\r\n" );
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document.write( "The height of the trapezoid CE is the leg of the right angled triangle BCE and its length is equal to   =  =  = 8 cm.\r\n" );
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document.write( "Now from the right-angled triangle AEC you have\r\n" );
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document.write( "    AC =  =  =  =  =  =  = .\r\n" );
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document.write( "Thus the diagonal of the trapezoid AC is   cm long.   ANSWER\r\n" );
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