Geometry Pdf 167998 | Math 348 Lecture 14

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File: Geometry Pdf 167998 | Math 348 Lecture 14

1 euclidean geometry 1 4 geometric gems the nine point circle nowwecometooneoftherealgemsofgeometry atheoremwhichwasdiscoveredmorethantwothousand years after euclid s day remember that for every three points which do not lie on a ...

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...Euclidean geometry geometric gems the nine point circle nowwecometooneoftherealgemsofgeometry atheoremwhichwasdiscoveredmorethantwothousand years after euclid s day remember that for every three points which do not lie on a line there is unique passes through them four very rarely going to be all and if then those form special type of quadrilateral called cyclic given it already quite difcult must near impossible nd yet this precisely what theorem tells us we can associated any particular triangle choosetothinkabout ninepointcircletheorem let abc beatrianglewithaltitudes ad cf medians ax by cz andorthocentre h b c are midpoints ah bh ch respectively d e f x y zalllie obvious reasons z proof galore in problem fact six interested denedasmidpoints soitseemslikeaprimeopportunitytousethemidpointtheorem appliedintriangle abh weobtainthat isparallelto ab xy also parallel ach isparallel applied bch obtain insummary xyanda areparalleltoeachotherandto furthermore yandb xareparalleltoeach other h...

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Posted on: 25 Jan 2023 | 2 years ago
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