document.write( "Question 108743: the shortest distance from the centre of a circle to a chord is 5 cm. find teh radius (2d.p.) of the circle if the chord is 3*2 times longer than the radius. \n" ); document.write( "

Algebra.Com's Answer #79298 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
I think the graph shows your problem.
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\n" ); document.write( "You form a right triangle with sides 5 and (6+R)/2, and a hypotenuse of R.
\n" ); document.write( "Using the Pythagorean theorem,
\n" ); document.write( " $\"%28%286%2BR%29%2F2%29%5E2%2B5%5E2=R%5E2\"$
\n" ); document.write( " $\"%28R%5E2%2B12R%2B36%29%2F4%2B25=R%5E2\"$ Expand the square.
\n" ); document.write( " $\"%28R%5E2%2B12R%2B36%29%2B100=4R%5E2\"$ Multiply both sides by 4.
\n" ); document.write( " $\"3R%5E2-12R-136=0\"$ Group all terms on one side.
\n" ); document.write( " $\"R+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"R+=+%28-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2-4%2A3%2A%28-136%29+%29%29%2F%282%2A3%29+\"$
\n" ); document.write( " $\"R+=+%28%2812%29+%2B-+sqrt%28+%28144%2B1632%29%29%29%2F%286%29+\"$
\n" ); document.write( " $\"R+=+%28%2812%29+%2B-+sqrt%28+%281776%29%29%29%2F%286%29+\"$
\n" ); document.write( " $\"R+=+%28%2812%29+%2B-+42.14%29%2F%286%29+\"$
\n" ); document.write( " $\"R+=+%28%2812%29+%2B+42.14%29%2F%286%29+\"$ Use only positive root, negative radius does not make sense in this application.
\n" ); document.write( " $\"highlight%28R=9.02%29\"$
\n" ); document.write( "Check your answer.
\n" ); document.write( " $\"%28%286%2BR%29%2F2%29%5E2%2B5%5E2=R%5E2\"$
\n" ); document.write( " $\"%28%286%2B9.02%29%2F2%29%5E2%2B5%5E2=%289.02%29%5E2\"$
\n" ); document.write( " $\"%287.51%29%5E2%2B5%5E2=%289.02%29%5E2\"$
\n" ); document.write( " $\"56.4%2B25=81.4\"$
\n" ); document.write( " $\"81.4=81.4\"$
\n" ); document.write( "True statement.
\n" ); document.write( "Good answer.
\n" ); document.write( "R=9.02 cm. \n" ); document.write( "

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