document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134517>Question 1134517</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello!<BR>\n" );
document.write( "I was having some trouble with one of my geometry homework problems. Here is the problem:\r<BR>\n" );
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document.write( "In pyramid ABCP, point M is the midpoint of BC. The segment PM is perpendicular to the plane of the base and PM = 9 cm. The radius of the circle circumscribed around ∆ABC is 24 cm and m∠CAB = 30°. Find the length of edge PB.\r<BR>\n" );
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document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #751934 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=751934\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Interesting problem.  I solved it using trigonometry; the result suggested a solution using only geometry should be possible, so I went back and found one.<br><BR>\n" );
document.write( "Let O be the center of the circumscribed circle, so OA=OB=OC=24.<br><BR>\n" );
document.write( "We are told that angle CAB is 30 degrees.  It is an angle inscribed in the circle.  Angle COB is an central angle cutting off the same arc as angle CAB, so angle COB is 60 degrees.<br><BR>\n" );
document.write( "Triangle COB is isosceles; M is the midpoint of the base.  So triangles COM and BOM are congruent right triangles, with angles COM and BOM each 30 degrees (half of angle COB).<br><BR>\n" );
document.write( "Now you have enough information to find the length of BM and CM.<br><BR>\n" );
document.write( "Finally, angle BMP is a right angle, so you can find the length of PB using the Pythagorean Theorem. </SPAN>\n" );
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