See complete Problem 137
Orthic Triangle, Altitudes, Perpendicular, Incircle, Collinear Points, Parallelogram. Level: High School, SAT Prep, College geometry
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Monday, July 21, 2008
Elearn Geometry Problem 137
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DM = GK (from P135) =>
ReplyDeleteGM = DK & G,N,H,M,K,D in a circle ( P 136)
=>
MK//GD (1) ( GMDK trapezoid cyclic)
=>
KM perpen BE (2)
ML perpen BE (3) ( EHLM kite )
(2) & (3) =>
K,M,L colline (4)
=>
KL//GD (5)
NGE = NDA ( have same arc NH )
A + ABE = 90°
BDN + NDA = A + NDA = A + NGE ( BDN = A P134 )
=>
NGE = ABE =>
NG//AB (6)
LN //AB (7) ( LN perp FC, FLHN kite)
(6) & (7) =>
G,N,L collin
2)
LK//GD//AC (8) ( from (5) & GD//AC )
LG//AB//KD (9) ( from (6) & (7) & DK//AB)
3)
LGDK paralelogr (10) ( from (8)&(9) )
GL = GM = DK ( from (10) & (1)
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