document.write( "Question 1149672: Medians AD, BE, and CF of triangle ABC meet at G, EF intersects AD at H, and AD=18. Find GH.\r
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Algebra.Com's Answer #771018 by ikleyn(52790) $\"\"$ $\"About$

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document.write( "Segment FE is the mid line in triangle ABC; therefore, line FE is parallel to BC.\r\n" );
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document.write( "Hence, triangles ABC and AFE are similar with the similarity coefficient 2 (from larger to smaller).\r\n" );
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document.write( "From it, you easily deduce that the length of AG is half of the length of AD; thus the length of AG is 18/2 = 9.\r\n" );
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document.write( "The intersection point divides the medians in proportion 2:1; therefore, the length of GD is 1/3 of the length AD;\r\n" );
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document.write( "thus the length of GD is 6 units.\r\n" );
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document.write( "It implies that the length of GF is  9-6 = 3 units.    ANSWER\r\n" );
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