document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=392130>Question 392130</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello tutor,<BR>\n" );
document.write( "This one question on my online homework assignment has been puzzling me for a while.\r<BR>\n" );
document.write( "\n" );
document.write( "A circle is given centered at (0,0)with a radius of 2.\r<BR>\n" );
document.write( "\n" );
document.write( "A line cuts through the center of the circle (slope of line unknown) but the line makes an angle of pi/3 with the x axis in the fourth quadrant.\r<BR>\n" );
document.write( "\n" );
document.write( "This line continues and cuts through point Q (coordinates unknown) of the circle in the fourth quadrant.<BR>\n" );
document.write( "------------------------------------------------------------------------------<BR>\n" );
document.write( "Another line forms a tangent to the circle at point Q and is perpendicular to the original line.\r<BR>\n" );
document.write( "\n" );
document.write( "this second line ( which is tangent to the circle and perpendicular to the original line) continues and crosses the x axis at some point P (coordinates unknown)\r<BR>\n" );
document.write( "\n" );
document.write( "* note that both lines share a point Q which lies on the circle.\r<BR>\n" );
document.write( "\n" );
document.write( "We are asked to ultimately find the coordinates of point P (x , 0)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------------------------------------------------<BR>\n" );
document.write( "there is an order of steps we have to perform.\r<BR>\n" );
document.write( "\n" );
document.write( "a)Find the coordinates of the point Q (x,y)\r<BR>\n" );
document.write( "\n" );
document.write( "b)Knowing two points on the original line, namely (0,0) and Q,compute the slope of the dotted line\r<BR>\n" );
document.write( "\n" );
document.write( "c)Knowing the slope of the first line, Compute the slope of the second line (which is perpendicular to the first line)\r<BR>\n" );
document.write( "\n" );
document.write( "d)We now know the point Q on the second line and the slope of the second line, so we find the equation of the line in the form <BR>\n" );
document.write( "y=mx+b\r<BR>\n" );
document.write( "\n" );
document.write( "e) therefor the coordinates of point P are (x,0) (Find x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #284676 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=284676\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A circle is given centered at (0,0)with a radius of 2.<BR>\n" );
document.write( "A line cuts through the center of the circle (slope of line unknown) but the line makes an angle of pi/3 with the x axis in the fourth quadrant.<BR>\n" );
document.write( "This line continues and cuts through point Q (coordinates unknown) of the circle in the fourth quadrant.<BR>\n" );
document.write( "------------------------------------------------------------------------------<BR>\n" );
document.write( "Another line forms a tangent to the circle at point Q and is perpendicular to the original line.<BR>\n" );
document.write( "this second line ( which is tangent to the circle and perpendicular to the original line) continues and crosses the x axis at some point P (coordinates unknown)<BR>\n" );
document.write( "* note that both lines share a point Q which lies on the circle.<BR>\n" );
document.write( "We are asked to ultimately find the coordinates of point P (x , 0)\r<BR>\n" );
document.write( "\n" );
document.write( "..\r<BR>\n" );
document.write( "\n" );
document.write( "According to the information given, I ended with a right triangle in quadrant IV, labeled as follows\"\r<BR>\n" );
document.write( "\n" );
document.write( "O - center of circle<BR>\n" );
document.write( "Q - point on circle where second line is tangent to circle and perpendicular to first line which goes thru origin.<BR>\n" );
document.write( "P - point at which second line crosses x-axis\r<BR>\n" );
document.write( "\n" );
document.write( "Angle at O - 60 deg<BR>\n" );
document.write( "Angle at P - 30 deg<BR>\n" );
document.write( "Angle at Q - 90 deg\r<BR>\n" );
document.write( "\n" );
document.write( "Line segment OQ is equal to the radius = 2<BR>\n" );
document.write( "since the reference angle of the first line is pi/3 = 60 deg, the angle at P must be 30 deg. This makes OP, the hypotenuse of the triangle twice that of OQ, being that OQ is opposite a 30 degree angle.  Therefore the hypotenuse is = 4.\r<BR>\n" );
document.write( "\n" );
document.write( "..\r<BR>\n" );
document.write( "\n" );
document.write( "ans: The coordinates at point P is (4,0) <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );