document.write( "Question 6543: Show that quadrilateral ABCD can be inscribed in a circle if and only if angle B and angle D are supplementary.\r
\n" ); document.write( "\n" ); document.write( "Hint: To proveif, show that D lies on the unique circle through A, B, and C.
\n" ); document.write( "Note: A quadrilateral inscribed in a cricle is said to be cyclic. \n" ); document.write( "
Algebra.Com's Answer #3573 by khwang(438)\"\" \"About 
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Here I you the sketch of the proof:\r
\n" ); document.write( "\n" ); document.write( " Show that quadrilateral ABCD can be inscribed in a circle if and only if angle B and angle D are supplementary.\r
\n" ); document.write( "\n" ); document.write( " --> If ABCD can be inscribed in a circle , then
\n" ); document.write( " angle ABC = 1/2 arc BDC and angle ADC = 1/2 arc ABC.
\n" ); document.write( " But, arc BDC + arc ABC = whole circle = 360 deg
\n" ); document.write( " Hence, angle B + angle D = 180 deg\r
\n" ); document.write( "\n" ); document.write( " <-- Draw a circle pass through A,B & C.
\n" ); document.write( " If point D is lying inside the circle,then
\n" ); document.write( " angle D + angle B > 180 (why?, hint: by extension line AD to
\n" ); document.write( " intersect the circle at point E)
\n" ); document.write( " If point D is lying outside the circle,then
\n" ); document.write( " angle D + angle B < 180 (why?)
\n" ); document.write( " Hence, we conclude that D must be lying on the circle.\r
\n" ); document.write( "\n" ); document.write( " Kenny\r
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