document.write( "Question 1158197: A circle goes through the points A, B, C, and D consecutively. The chords AC and BD intersect at P. Given that AP = 6, BP = 8, and CP = 3, how long is DP? \n" ); document.write( "

Algebra.Com's Answer #781106 by ikleyn(52835) $\"\"$ $\"About$

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document.write( "For these chords and their parts, there is this metric relation\r\n" );
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document.write( "    |AP| * |CP| = |BP| * |DP|,   \r\n" );
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document.write( "or\r\n" );
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document.write( "    6 * 3 = 8 * |DP|,\r\n" );
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document.write( "which gives you  |DP| =  =  = .    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "See the lesson\r
\n" ); document.write( "\n" ); document.write( "    - The parts of chords that intersect inside a circle, \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "For theory lessons in this site on circles, their chords, secant and tangent lines see \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
\n" ); document.write( "\n" ); document.write( "    - Quadrilateral circumscribed about a circle\r
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\n" ); document.write( "\n" ); document.write( "For lessons on solved problems for circles, their chords, secant and tangent lines see\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
\n" ); document.write( "\n" ); document.write( "in this site.\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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