document.write( "Question 1184286: If four distinct points (2k, 3k), (2, 0), (0, 3) and (0, 0) lie on circle then which condition is true from the following:
\n" ); document.write( "A- k < 0
\n" ); document.write( "B- 0 < k < 1
\n" ); document.write( "C- k = 1
\n" ); document.write( "D- k > 1 \n" ); document.write( "

Algebra.Com's Answer #814827 by ikleyn(52794) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "If four distinct points (2k, 3k), (2, 0), (0, 3) and (0, 0) lie on circle then which condition is true from the following:
\n" ); document.write( "A- k < 0
\n" ); document.write( "B- 0 < k < 1
\n" ); document.write( "C- k = 1
\n" ); document.write( "D- k > 1
\n" ); document.write( "~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Straight line segment connecting the points (2,0) and (0,0) is horizontal  y= 0;\r\n" );
document.write( "\r\n" );
document.write( "    hence, the center of the circle lies at the perpendicular bisector x = 1.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Straight line segment connecting the points (0,3) and (0,0) is vertical  x= 0;\r\n" );
document.write( "\r\n" );
document.write( "    hence, the center of the circle lies at the perpendicular bisector y = 1.5.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "        It implies that the center of the circle is the point  (1,1.5).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus we see, that three points  (0,0) (at the circle),  (1.1.5) (the circle center)  and  (2k,3k) (at the circle)  all lie \r\n" );
document.write( "\r\n" );
document.write( "on the same straight line  y =   (the circle's diameter).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It may happen if and only if  k = 0  or  k = 1.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The case  k = 0  leads to the existing point (0,0).  \r\n" );
document.write( "\r\n" );
document.write( "Since from the context, the point (2k,3k) is distinct from (0,0), it leaves only one remaining possibility for k to be equal to 1:  k = 1.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The only option is  C :  k = 1.\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Solved, answered and explained.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );