excircle - Maple Help

geometry

 excircle
 find three excircles of a given triangle

 Calling Sequence excircle(obj, T, n)

Parameters

 obj - list of three excircles to be created T - triangle n - (optional) a list of three elements and of the form $\left[\mathrm{c1}\left(\mathrm{o1}\right),\mathrm{c2}\left(\mathrm{o2}\right),\mathrm{c2}\left(\mathrm{o2}\right)\right]$ where c1, c2, c2, o1, o2, o3 are names.

Description

 • A circle tangent to one side of a triangle and to the extensions of the other two sides is called an excircle of the triangle.
 • The routine returns obj which is a list of three excircles of triangle T.
 • If the optional argument n is given, the names of the three excircles will be c1, c2, c3; while the names of their centers in that order will be o1, o2, o3.
 • For a detailed description of the excircles obj, use the routine detail (i.e., detail(obj))
 • Note that the routine only works if the vertices of the triangle are known.
 • The command with(geometry,excircle) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{ps}≔\mathrm{point}\left(A,1,1\right),\mathrm{point}\left(B,3,1\right),\mathrm{point}\left(C,2,4\right):$
 > $\mathrm{triangle}\left(T,\left[\mathrm{ps}\right]\right)$
 ${T}$ (1)
 > $\mathrm{excircle}\left(\mathrm{obj},T,\left[\mathrm{c1}\left(\mathrm{o1}\right),\mathrm{c2}\left(\mathrm{o2}\right),\mathrm{c3}\left(\mathrm{o3}\right)\right]\right)$
 $\left[{\mathrm{c1}}{,}{\mathrm{c2}}{,}{\mathrm{c3}}\right]$ (2)
 > $\mathrm{draw}\left(\left\{T,\mathrm{op}\left(\mathrm{obj}\right)\right\},\mathrm{printtext}=\mathrm{true}\right)$
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 8, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8942753672599792, "perplexity": 929.529947476595}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662521152.22/warc/CC-MAIN-20220518052503-20220518082503-00612.warc.gz"}