document.write( "Question 190350: in circle o, chords AB and CD intersect at E. if AE=10, EB=6 & CE is 2 more than twice ED, find CE and ED \n" ); document.write( "

Algebra.Com's Answer #142890 by orca(409) $\"\"$ $\"About$

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Let ED = x.
\n" ); document.write( "Then CE = 2x + 2
\n" ); document.write( "According to the chord segment theorem in geometry, (CE)(DE)=(AE)(BE)
\n" ); document.write( "By substitution, we have
\n" ); document.write( " $\"%282x%2B2%29x=6%2A10\"$
\n" ); document.write( "Simplifying, we get
\n" ); document.write( " $\"2%28x%2B1%29x=6%2A10\"$
\n" ); document.write( " $\"%28x%2B1%29x=30\"$ dividing both sides by 2\r
\n" ); document.write( "\n" ); document.write( "Re-write it in standard form, we have:
\n" ); document.write( " $\"x%5E2%2Bx-30=0\"$
\n" ); document.write( "Solving for x, we have
\n" ); document.write( " $\"%28x-5%29%28x%2B6%29=0\"$
\n" ); document.write( "So x = 5 or x= -6 (reject this negative number)
\n" ); document.write( "Thus DE = 5. Therefore CE =2x + 2 = 12.
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