document.write( "Question 1069371: The radius of two concentric circles are 13cm and 8cm . AB is a diamerer of the bigger circle and BD is tangent to the smaller circle touching it at D. And intersecting the larger circle at P on producing. Find the length of AP\r
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Algebra.Com's Answer #684582 by ikleyn(52832) $\"\"$ $\"About$

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\n" ); document.write( "Answer. The length of AP is 13: |AP| = 13 cm.\r
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document.write( "Consider two triangles, ODB and ABP, where O is the common center of the circles.\r\n" );
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document.write( "The triangle OBD is a right-angled triangle with the right angle at the vertex D, since the radius drawn to the tangent point \r\n" );
document.write( "is perpendicular to the tangent line.\r\n" );
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document.write( "The triangle ABP is also a right-angled triangle with the right angle at the vertex P, since the angle APB lean on the diameter of the circle.\r\n" );
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document.write( "These two triangles are similar since they have the common acute angle ABP (same as OBD). \r\n" );
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document.write( "The similarity coefficient is 2:  =  = 2: it is the ratio of hypotenuses of the triangles.\r\n" );
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document.write( "Therefore, |AP| = 2.|OD| = 2*8 = 16 cm.\r\n" );
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document.write( "Answer.  |AP| = 16 cm.\r\n" );
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\n" ); document.write( "\n" ); document.write( "For properties of circles, their radii and tangent lines, that relevant to this problem, see the lessons \r
\n" ); document.write( "\n" ); document.write( "    - A tangent line to a circle is perpendicular to the radius drawn to the tangent point \r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook on Geometry\r
\n" ); document.write( "\n" ); document.write( "    GEOMETRY - YOUR ONLINE TEXTBOOK \r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part if this textbook under the topic
\n" ); document.write( "\"Properties of circles, inscribed angles, chords, secants and tangents\".\r
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