b*k
发帖数: 27 | 1 Two circles T1 and T2 intersect at M and N.
Let L be the common tangent to T1 and T2 so that M is closer to
L than N is. Let L touch T1 at A and T2 at B. Let the line through M parallel
to L meet the circle T1 again at C and circle T2 at D.
Lines CA and DB meet at E; lines AN and CD meet at P; lines BN and CD meet at
Q.
show that EP = EQ | l**n
发帖数: 67 | 2 1.EM is perpendicular to AB (in triangle ECD, CA = AM, DB = BM)
2.PM = MQ (MN 平分AB,PQ)
=>EP = EQ
【在 b*k 的大作中提到】
: Two circles T1 and T2 intersect at M and N.
: Let L be the common tangent to T1 and T2 so that M is closer to
: L than N is. Let L touch T1 at A and T2 at B. Let the line through M parallel
: to L meet the circle T1 again at C and circle T2 at D.
: Lines CA and DB meet at E; lines AN and CD meet at P; lines BN and CD meet at
: Q.
: show that EP = EQ
| u**x
发帖数: 45 | 3 设原心 O1, O2,
1)
由O1A, O2B 垂直平分CM, MD
则AB=1/2CD
CA=E, DB=BE,
有EM//OA1//OA2, EM垂直CD.
2) 延MN交AB于G. GA^2=GB^2=GM*GN
GA=GB
又PM/GA=QM/GB
PM=QM
由1)2) EP=EQ |
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