document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=60904>Question 60904</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a line through the center of a circle is perpendicular to a chord, then the line also bisects the chord.\r<BR>\n" );
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document.write( "I have some work done with a drawing on sketchpad, but I am not sure where to even start with writing my proof. They make no sense to me since I have not had a good teacher to teach me proofs. Thank you  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #41855 by </B><A HREF=/tutors/aboutme.mpl?userid=asha><B>asha(30)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=asha><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=41855\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let AB be a chord in the circle<BR>\n" );
document.write( "let line XY intersect the chord at P.<BR>\n" );
document.write( "let O be the centre of the circle.<BR>\n" );
document.write( "OP is perpendicular to AB.<BR>\n" );
document.write( "Join OA and OB.<BR>\n" );
document.write( "you have 2 right angled triangles OAP and OBP.<BR>\n" );
document.write( "Considering the two triangles, we have<BR>\n" );
document.write( "OA = OB   radii of the circle and the hypotenuse of the right triangles.<BR>\n" );
document.write( "OP is common to the two triangles.<BR>\n" );
document.write( "angle OPA = angle OPB =90 degrees. <BR>\n" );
document.write( "therefore the two triangles are congruent.(right angle, hypotenuse and side)<BR>\n" );
document.write( "hence AP =PB  (corresponding parts of congruent triangles are equal)<BR>\n" );
document.write( "the line OP bisects chord AB. </SPAN>\n" );
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