Geometry Problem

Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the complete problem 629.

## Thursday, June 23, 2011

### Problem 629: Triangle, Perpendicular to Sides, Intersecting Lines, Altitude

Labels:
altitude,
intersecting lines,
perpendicular,
side,
triangle

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analytic geometry ??

ReplyDeletelet be

A(0,0)B(a,b)C(c,0)D(0,d)E(c,e)

line AE:y=ex/c

line DC:y=-dx/c+d

line DB:y=(b-d)x/a+d

line BE:y=(e-b)(x-c)/(c-a)+e

point F: xF=-acd/(bc-cd-ea) yF=-aed/(bc-cd-ea)

point G: xG=(ad-ae+bc-cd)c/(ad+bc-dc-ec)

yG=(a-c)de/(ad+bc-dc-ec)

line AG:y=(a-c)dex/((ad-ae+bc-cd)c)

line FC:y=yF(x-c)/(xF-c)

intersection AG ,CF: xH=a

BH//AD//CE

we dont have used the right angles, this property remains with DA //CE

To Anonymous (Problem 629): Thanks for your comments. You are right, the property remains with DA//CE. See Geometry Problem 633.

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