document.write( "Question 1202157: Two chords, AD and BC of a circle intersect at a point O inside the circle. Given that BO=5cm, OD=3cm and CD=3.6 cm, calculate the length AB \n" ); document.write( "

Algebra.Com's Answer #836822 by ikleyn(52797) $\"\"$ $\"About$

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\n" ); document.write( "Two chords, AD and BC of a circle intersect at a point O inside the circle.
\n" ); document.write( "Given that BO = 5 cm, OD = 3 cm and CD = 3.6 cm, calculate the length AB.
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document.write( "Make a sketch, drawing the circle, the chords and marking the points.\r\n" );
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document.write( "Consider triangles AOB and DOC.\r\n" );
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document.write( "These triangles are similar.\r\n" );
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document.write( "Indeed, their angles AOB and DOC are congruent, since they are vertical angles.\r\n" );
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document.write( "Angles BAO and OCD are congruent, too, because the angles BAD and BCD are inscribed angles\r\n" );
document.write( "leaning on the same arc BD of the circle.\r\n" );
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document.write( "It is just enough for the proof that triangles AOB and DOC are similar, having two pairs \r\n" );
document.write( "of congruent angles.\r\n" );
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document.write( "From the triangle similarity, the corresponding pairs of sides are (BO,OD) and (AB,CD),\r\n" );
document.write( "so we can write a proportion\r\n" );
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document.write( "     = .\r\n" );
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document.write( "Substituting the values, we get\r\n" );
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document.write( "     = .\r\n" );
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document.write( "It gives  AB =  =  = 6.\r\n" );
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document.write( "ANSWER.  AB = 6 cm.\r\n" );
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