document.write( "Question 1158593: .Find the radius of the largest circle that can be drawn inside the right triangle that has
\n" ); document.write( "6-cm and 8-cm legs. \n" ); document.write( "
Algebra.Com's Answer #781591 by ikleyn(52798)\"\" \"About 
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document.write( "Hypotenuse of this right triangle is (OBVIOUSLY) 10 centimetres, since this triangle is (3-4-5) right angled triangle.\r\n" );
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document.write( "Now, in Geometry there is a general theorem, stating that\r\n" );
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document.write( "    for any right triangle, the radius of the inscribed circle  \" r \"  is\r\n" );
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document.write( "        r = \"%28a%2Bb-c%29%2F2\",\r\n" );
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document.write( "    where \"a\" and \"b\" are the measures of the legs, and c is the measure of the hypotenuse.\r\n" );
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document.write( "In your case,  r = \"%286+%2B+8+-+10%29%2F2\" = \"4%2F2\" = 2.\r\n" );
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document.write( "ANSWER.  The radius of the inscribed circle is  2 centimetres.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On the Theorem, referred above, see the lesson\r
\n" ); document.write( "\n" ); document.write( "    - The radius of a circle inscribed into a right angled triangle \r
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\n" ); document.write( "\n" ); document.write( "My theory lessons in this site on circles, their chords, secant and tangent lines are \r
\n" ); document.write( "\n" ); document.write( "    - A circle, its chords, tangent and secant lines - the major definitions, \r
\n" ); document.write( "\n" ); document.write( "    - The longer is the chord the larger its central angle is, \r
\n" ); document.write( "\n" ); document.write( "    - The chords of a circle and the radii perpendicular to the chords, \r
\n" ); document.write( "\n" ); document.write( "    - A tangent line to a circle is perpendicular to the radius drawn to the tangent point, \r
\n" ); document.write( "\n" ); document.write( "    - An inscribed angle in a circle, \r
\n" ); document.write( "\n" ); document.write( "    - Two parallel secants to a circle cut off congruent arcs, \r
\n" ); document.write( "\n" ); document.write( "    - The angle between two chords intersecting inside a circle, \r
\n" ); document.write( "\n" ); document.write( "    - The angle between two secants intersecting outside a circle, \r
\n" ); document.write( "\n" ); document.write( "    - The angle between a chord and a tangent line to a circle, \r
\n" ); document.write( "\n" ); document.write( "    - Tangent segments to a circle from a point outside the circle, \r
\n" ); document.write( "\n" ); document.write( "    - The converse theorem on inscribed angles, \r
\n" ); document.write( "\n" ); document.write( "    - The parts of chords that intersect inside a circle, \r
\n" ); document.write( "\n" ); document.write( "    - Metric relations for secants intersecting outside a circle  and \r
\n" ); document.write( "\n" ); document.write( "    - Metric relations for a tangent and a secant lines released from a point outside a circle \r
\n" ); document.write( "\n" ); document.write( "    - Quadrilateral inscribed in a circle\r
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\n" ); document.write( "\n" ); document.write( "To see solved problems for circles, their chords, secant and tangent lines, look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO bisect an arc in a circle using a compass and a ruler, \r
\n" ); document.write( "\n" ); document.write( "    - HOW TO find the center of a circle given by two chords, \r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on a radius and a tangent line to a circle, \r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on inscribed angles, \r
\n" ); document.write( "\n" ); document.write( "    - A property of the angles of a quadrilateral inscribed in a circle, \r
\n" ); document.write( "\n" ); document.write( "    - An isosceles trapezoid can be inscribed in a circle, \r
\n" ); document.write( "\n" ); document.write( "    - HOW TO construct a tangent line to a circle at a given point on the circle, \r
\n" ); document.write( "\n" ); document.write( "    - HOW TO construct a tangent line to a circle through a given point outside the circle, \r
\n" ); document.write( "\n" ); document.write( "    - HOW TO construct a common exterior tangent line to two circles, \r
\n" ); document.write( "\n" ); document.write( "    - HOW TO construct a common interior tangent line to two circles, \r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on chords that intersect within a circle, \r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on secants that intersect outside a circle, \r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on a tangent and a secant lines released from a point outside a circle  and \r
\n" ); document.write( "\n" ); document.write( "    - The radius of a circle inscribed into a right angled triangle (*)\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on tangent lines released from a point outside a circle\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 of this online textbook under the topic  \"Properties of circles, inscribed angles, chords, secants and tangents \".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in GEOMETRY
\n" ); document.write( "https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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