Inviato: 01 gen 1970, 01:33
USAMO \'98
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<BR>2. Let C1 and C2 be concentric circles, with C2 in the interior of C1. From a point A on C1 one draws the tangent AB to C2 (B on C2).
<BR>Let C be the second point of intersection of AB and C1, and let D be the midpoint of AB. A line passing through A intersects C2 at E and F in such a way that the perpendicular bisectors of DE and CF intersect at a point M on AB. Find, with proof, the ratio AM/MC.
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<BR><font size=1>[ This message was edited by: sprmnt21 on 2002-01-23 16:56 ]</font>
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<BR><font size=1>[ This message was edited by: sprmnt21 on 2002-01-23 16:57 ]</font>
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<BR><font size=1>[ This message was edited by: sprmnt21 on 2002-01-23 17:13 ]</font><BR><BR><font size=1>[ This message was edited by: sprmnt21 on 2002-01-23 17:23 ]</font>
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<BR>2. Let C1 and C2 be concentric circles, with C2 in the interior of C1. From a point A on C1 one draws the tangent AB to C2 (B on C2).
<BR>Let C be the second point of intersection of AB and C1, and let D be the midpoint of AB. A line passing through A intersects C2 at E and F in such a way that the perpendicular bisectors of DE and CF intersect at a point M on AB. Find, with proof, the ratio AM/MC.
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<BR><font size=1>[ This message was edited by: sprmnt21 on 2002-01-23 16:56 ]</font>
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<BR><font size=1>[ This message was edited by: sprmnt21 on 2002-01-23 16:57 ]</font>
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<BR><font size=1>[ This message was edited by: sprmnt21 on 2002-01-23 17:13 ]</font><BR><BR><font size=1>[ This message was edited by: sprmnt21 on 2002-01-23 17:23 ]</font>