document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203424>Question 1203424</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Right triangle $ABC$ has $AB = AC = 6$ cm. Circular arcs are drawn with centers at $A, B$ and $C,$ so that the arc centered at $A$ is tangent to side $BC$ and so that the arcs centered at $B$ and $C$ are tangent to the arc centered at $A,$ as shown. What is the perimeter of the shaded region? Express your answer as a decimal to the nearest hundredth.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "https://ibb.co/YXDJKRj </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838993 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=838993\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Use the pythagorean theorem to find that hypotenuse BC = 6*sqrt(2)<BR>\n" );
document.write( "Or you can use the 45-45-90 triangle template.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let D = midpoint of B and C\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "It turns out that any right triangle will have its circumcenter at the midpoint of the hypotenuse.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This means we can draw a circle centered at D, and radius 3*sqrt(2). <BR>\n" );
document.write( "This circumcircle passes through A, B, and C.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The distance from A to D is 3*sqrt(2), aka the radius of this new circle.<BR>\n" );
document.write( "Therefore, segment AD = 3*sqrt(2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use this info to determine the radius of each small arc. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To get the distance along a circle's edge, you'll need this formula<BR>\n" );
document.write( "arc length = (angle in radians)*r\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "45 degrees = pi/4 radians<BR>\n" );
document.write( "90 degrees = pi/2 radians\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I'll let the student finish up from here.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );