document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148142>Question 148142</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The diagonals of rhombus ABCD meet at M. Angle DAB measures 60 degrees. Let P be the midpoint of AD and let G be the intersection of PC and MD. Given that AP = 8, find MD, MC, MG, CG, and GP.\r<BR>\n" );
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document.write( "thank you all veryyyy much ! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108566 by </B><A HREF=/tutors/aboutme.mpl?userid=orca><B>orca(409)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=orca><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=108566\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The two diagonals are perpendicular and bisect each other.<BR>\n" );
document.write( "As AB = AC and < A = 60, Triangle ABD is equilateral.<BR>\n" );
document.write( "AB = BD = AD = 2*AP = 16<BR>\n" );
document.write( "MD = BD/2 = 8<BR>\n" );
document.write( "MC = AM = sqrt(AD^2 - MD^2) = sqrt(16^2 - 8^2) = 8*sqrt(3)<BR>\n" );
document.write( "In triangle ADC, MD and PC are medians, G is centroid of the triangle. So<BR>\n" );
document.write( "MG = MD/3 = 8/3<BR>\n" );
document.write( "CG = sqrt(MC^2 + MG^2)<BR>\n" );
document.write( "= sqrt{[8sqrt(3)]^2 + (8/3)^2}<BR>\n" );
document.write( "= sqrt[(8^2)(3 + 1/9]<BR>\n" );
document.write( "= sqrt[(8^2)(28/9]<BR>\n" );
document.write( "= (8/3)sqrt(28)<BR>\n" );
document.write( "= (16/3)sqrt(7)<BR>\n" );
document.write( "As G is the centroid, GP = CG/2 = (8/3)sqrt(7)<BR>\n" );
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