document.write( "Question 1148427: Equilateral triangle ABC has sides of 22cm. A circle of radius 5 cm inside it is tangent to sides AB & AC. Find the distance from the circle’s center to side BC, in cm. \n" ); document.write( "

Algebra.Com's Answer #769779 by ikleyn(52787) $\"\"$ $\"About$

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

\r\n" );
document.write( "\r\n" );
document.write( "The altitude of the triangle ABC from vertex A, drawn to the side BC  is  \r\n" );
document.write( "\r\n" );
document.write( "    h =  cm.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let the center of the circle be the point O at this altitude.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "And let the points D and E are the tangent points at the sides AB and AC.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then the triangle ODA is a right angled triangle with the shorter leg of 5 cm and the acute angle OAD of 30 degrees.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence, its hypotenuse OA is twice the radius. i.e. 10 cm.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus the distance from the center O of the circle to the side BC is\r\n" );
document.write( "\r\n" );
document.write( "    d =  - 10 cm = 19.053 - 10 = 9.053 cm.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The distance from the center O of the circle to the side BC is  d =  - 10 cm = 9.053 cm.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );