document.write( "Question 1043931: ABCD is a cyclic quadrilateral, angle DAB =80 and angle ACB =50 .
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Algebra.Com's Answer #659166 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "ABCD is a cyclic quadrilateral, angle DAB =80 and angle ACB =50 .
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document.write( "Let me remind you that a cyclic quadrilateral is a quadrilateral inscribed into the circle.\r\n" );
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document.write( "So, ABSD is inscribed into a circle. \r\n" );
document.write( "Then the measure of the angle DAB plus the measure of the opposite angle BCD is 180°.\r\n" );
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document.write( "    (If a quadrilateral is inscribed into a circle, then the sum of the measures of its opposite angles is 180°.  \r\n" );
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document.write( "    See the lesson Quadrilateral inscribed in a circle in this site).\r\n" );
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document.write( "So,  mLDAB + mLBCD = 180°.\r\n" );
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document.write( "But  mLBCD = mLACB + mLACD.\r\n" );
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document.write( "Therefore,  mLDAB + mLACB + mLACD = 180°.\r\n" );
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document.write( "But  mLDAB + mLACB = 80° + 50° = 130°.\r\n" );
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document.write( "Therefore,  mLACD = 180° - 130° = 50°.\r\n" );
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document.write( "Thus the inscribed angles  LACB  and  LACD  have equal measures.\r\n" );
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document.write( "Hence, they lean equal arcs: the length of the arc AB is the same as the length of the AD.\r\n" );
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document.write( "It implies that the chords AB and AD have equal lengths.   QED.\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 lessons associated with it:\r
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\n" ); document.write( "\n" ); document.write( "    - Quadrilateral inscribed in a circle\r
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\n" ); document.write( "\n" ); document.write( "and \r
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\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( "    - An inscribed angle in a circle \r
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