document.write( "Question 1068288: Two circles intersect at A and B.From B two diameters BC and BD are drawn which cut the circles at C and D respectively.Prove that CAD is a straight line. \n" ); document.write( "

Algebra.Com's Answer #683525 by KMST(5328) $\"\"$ $\"About$

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A and B are points on both circles.
\n" ); document.write( "C is on one circle,
\n" ); document.write( "where BC is a diameter.
\n" ); document.write( "Since BC is a diameter, angle BAC is an inscribed angle
\n" ); document.write( "intercepting an arc that is half of that circle.
\n" ); document.write( "The measure of BAC is half of the intercepted arc,
\n" ); document.write( "or $\"180%5Eo%2F2=90%5Eo\"$ .
\n" ); document.write( "The same reasoning with diameter BD on the other circle
\n" ); document.write( "proves that angle BAD measures $\"90%5Eo\"$ .
\n" ); document.write( "Since BAC and BAD both measure $\"90%5Eo\"$ ,
\n" ); document.write( "their sum, angle CAD measures
\n" ); document.write( " $\"90%5Eo%2B90%5Eo=180%5Eo\"$ ,
\n" ); document.write( "meaning that rays AC and AD are two \"halves\" of the same line CD. \n" ); document.write( "

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