See complete Problem 137

Orthic Triangle, Altitudes, Perpendicular, Incircle, Collinear Points, Parallelogram. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

## Monday, July 21, 2008

### Elearn Geometry Problem 137

Labels:
altitude,
collinear,
incircle,
orthic triangle,
parallelogram,
perpendicular,
tangency point,
triangle

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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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