document.write( "Question 388149: Draw a circle with a diameter of 7 cm and a point,P, 10cm from the centre of this circle. Complete the diagram by adding the two tangents to the circle from the point P. Label the points of the tangency A and B) Provide sufficient additional information to determine the lengths of PA and PB. \n" ); document.write( "

Algebra.Com's Answer #275707 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "Let the center of the circle be O.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Draw in a radius to one of the points of tangency.  I'll draw OA.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "OA is perpendicular to AP because a radius drawn to the point\r\n" );
document.write( "of tangency is perpendicular to the tangent line.\r\n" );
document.write( "\r\n" );
document.write( "Therefore triangle OAP is a right triangle. Therefore we can use \r\n" );
document.write( "the Pythagorean theorem:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "BP is also \r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );