document.write( "Question 1085890: Points A, B, and C are on a circle such that AB = 8, BC = 15, and AC = 17. Find the radius of the circle. \n" ); document.write( "

Algebra.Com's Answer #699990 by ikleyn(52847) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "Notice that  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Indeed,  = 64 + 225 = 280 = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It means that the triangle ABC is a right-angled triangle with the right angle at the vertex B and AC is its hypotenuse.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "This right-angled triangle is inscribed into the circle.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It means that its hypotenuse AC is the diameter of the circle.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence, the radius of the circle is  = 8.5 units.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved. The radius of the circle is 8.5 units.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );