document.write( "Question 1187404: https://imgur.com/hrQkDYl (copy and paste this link into the search bar to view the diagram). In the diagram, circle with centre O has a radius of 5 cm. Segment AT is tangent to the circle. AO = 13 cm, and AX = XY (this length is labeled m). Find the length of m. \n" ); document.write( "

Algebra.Com's Answer #818374 by ikleyn(52815) $\"\"$ $\"About$

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\n" ); document.write( "In the diagram, circle with centre O has a radius of 5 cm.
\n" ); document.write( "Segment AT is tangent to the circle. AO = 13 cm, and AX = XY (this length is labeled m). Find the length of m.
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\n" ); document.write( "\n" ); document.write( " This problem is not difficult.\r
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document.write( "First of all, from triangle AOT,  AT =  =  =  = 12 cm.\r\n" );
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document.write( "Next, consider triangle XTO.\r\n" );
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document.write( "Its leg XT has the length (12-m)  cm.  It is the tangent segment to the circle O.\r\n" );
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document.write( "Continue XO further to intersection with the circle O.\r\n" );
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document.write( "You will get the long secant of the length  m+5+5 = m + 10 cm.\r\n" );
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document.write( "The outer part of this secant has the length m.\r\n" );
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document.write( "Using well known property of the tangent segment, secant and its outer part, you can write this equation\r\n" );
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document.write( "     = m*(m+10),  \r\n" );
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document.write( "which is\r\n" );
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document.write( "     = m*(m+10).\r\n" );
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document.write( "Simplify and find \"m\"\r\n" );
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document.write( "    144 - 24m + m^2 = m^2 + 10m\r\n" );
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document.write( "    144 = 10m + 24m\r\n" );
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document.write( "    144 = 34m\r\n" );
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document.write( "     m  =  =   cm = 4  cm.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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