document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138221>Question 1138221</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A circle has a chord of 25mm with an angle of pi/6 subtended at the centre. Find, to 1 dp, the length of the arc cut by the chord.\r<BR>\n" );
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document.write( "'m just not sure how to find the radius. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #756077 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=756077\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  see the attached diagram.\r<BR>\n" );
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document.write( "explanation is underneath.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/040411.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the subtending central angle is angle BAC which is equal to pi/6 radians.\r<BR>\n" );
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document.write( "the chord is BC which is 25 millimeters long.\r<BR>\n" );
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document.write( "if you draw a line from the center of the circle intersecting with the chord at 90 degrees, this will split the chord in half.\r<BR>\n" );
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document.write( "see the bottom part of the diagram to see what that looks like.\r<BR>\n" );
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document.write( "that will make BD = 12.5 and DC = 12.5 millimeters in length.\r<BR>\n" );
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document.write( "you will form an isosceles triangle with AB and AC as the legs of it.\r<BR>\n" );
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document.write( "AB and AC are also radii of the circle.\r<BR>\n" );
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document.write( "the vertex of this isosceles triangle is split in half forming right triangles ADB and ADC.\r<BR>\n" );
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document.write( "angles BAD and CAD are each equal to half of angle BAC which makes them equal to pi/12 radians each.\r<BR>\n" );
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document.write( "sin(BAD) is equal to sin(pi/12) which is equal to opposite / hypotenuse of triangle ADB which make it equal to 12.5 / R.\r<BR>\n" );
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document.write( "solve for R to get R = 12.5 / sin(pi/12) which makes it equal to 48.29629131 millimeters in length.\r<BR>\n" );
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document.write( "the circumference of the circle is equal to 2 * pi * R =  303.454548 millimeters.\r<BR>\n" );
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document.write( "the arc cut by a central angle of pi/6 radians has a length of (pi/6) / (2pi) * the circumference of the circle which is equal to (pi/6) / (2pi) * 303.454548 = 25.287879 millimeters in length.\r<BR>\n" );
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document.write( "that's the length of arc BC. which is the length of the arc cut by the chord.\r<BR>\n" );
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document.write( "round to one decimal place and the length of arc BC = 25.3 millimeters.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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