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Topic: Excircle

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	Incircle and excircles of a triangle - Wikipedia, the free encyclopedia
		An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two.
		The center of an excircle is the intersection of the internal bisector of one angle and the external bisectors of the other two.
		The radii of the in- and excircles are closely related to the area of the triangle.
	en.wikipedia.org /wiki/Excircle (515 words)

	Excircle
		In geometry an excircle or escribed circle of a triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two sides.
		Every triangle has three distinct excircles, each tangent to the side of the triangle it is associated with.
		The center of an excircle lies on the internal bisector of one angle and the external bisectors of the other two.
	www.ebroadcast.com.au /lookup/encyclopedia/ex/Excircle.html (72 words)

	Excircle of a Triangle (Site not responding. Last check: 2007-10-31)
		The excircle is the circle whose center is defined by the intersection of the external angle bisectors of two vertices A and B (angles
		The excircle is also tangent to the extension of the sides a and b.
		Note that the excircles are not necessarily tangent to the incircle.
	www.vias.org /comp_geometry/geom_triangle_excircle.html (105 words)

	Excircle Problems (Site not responding. Last check: 2007-10-31)
		Given triangle ABC with side lengths a, b, and c.
		Let circle O be an excircle and let X, Y, and Z be its points of tangency, as shown.
		(b) Prove that triangle XYZ is obtuse, that is, that the triangle determined by the points of tangency of an excircle is always obtuse.
	jwilson.coe.uga.edu /emt725/Bob2/excircle/excircle.html (160 words)

	Nine-point circle - Wikipedia, the free encyclopedia
		In 1822 Karl Feuerbach discovered that any triangle's nine-point circle is externally tangent to that triangle's three excircles and internally tangent to its incircle.
		If an orthocentric system of four points is given, then the four triangles formed by any combination of three distinct points of that system all have the same nine-point circle.
		The centers of the incircle and excircles of a corresponding triangle form an orthocentric system.
	en.wikipedia.org /wiki/Nine_point_circle (599 words)

	Incircles and Excircles in a Triangle
		From the just derived formulas it follows that the points of tangency of the incircle and an excircle with a side of a triangle are symmetric with respect to the midpoint of the side.
		The cevians joinging the two points to the opposite vertex are also said to be isotomic.
		For the incircle, the point is Gergonne'; for the points of excircle tangency, the point is Nagel's.
	www.cut-the-knot.org /triangle/InExCircles.shtml (254 words)

	Excircle and excenter (Site not responding. Last check: 2007-10-31)
		An excircle is a circle that is externally tangent to the sides of a triangle as shown in the figure below.
		The excenter is the center of that circle.
		On the same triangle, construct the 3 excircles, the incircle, and the nine-point circle.
	www.niles-hs.k12.il.us /timmil/pedal.htm (338 words)

	Incircle and excircles of a triangle (Site not responding. Last check: 2007-10-31)
		An excircle orescribed circle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangentto the extensions of the other two.
		The center of an excircle is the intersection of the internal bisector of one angle and the externalbisectors of the other two.
		From these formulas we see in particular that the excircles are always largerthan the incircle, and that the largest excircle is the one attached to the longest side.
	www.therfcc.org /incircle-and-excircles-of-a-triangle-214963.html (331 words)

	Incircle and excircles of a triangle - Biocrawler (Site not responding. Last check: 2007-10-31)
		Incircle and excircles of a triangle - Biocrawler
		The triangle's nine point circle is tangent to the three excircles as well as to the incircle.
		You can find it there under the keyword Excircle (http://en.wikipedia.org/wiki/Excircle)The list of previous authors is available here: version history (http://en.wikipedia.org/w/index.php?title=Excircleandaction=history).
	www.biocrawler.com /encyclopedia/Excircle (477 words)

	Incircle and excircles of a triangle (Site not responding. Last check: 2007-10-31)
		An excircle or escribed circle of the triangle is a circle outside the triangle tangent to one of sides and tangent to the extensions of other two.
		The center of an excircle the intersection of the internal bisector of angle and the external bisectors of the two.
		From these formulas we see in that the excircles are always larger than incircle and that the largest excircle is one attached to the longest side.
	www.freeglossary.com /Excircle (423 words)

	From Pentagon to Heptagon by Marcus the Marinite for the Nexus Network Journal vol.3 no.3 Summer 2001 (Site not responding. Last check: 2007-10-31)
		A beautiful relationship also exists within the pentagon in that the chord of the pentagon is the geometric mean between the extremes of the height of the pentagon and the diameter of the pentagon's excircle.
		Taking their half-lengths, GN and GB, we can generate two circles; that is, the circumscribing circle commonly termed the excircle, and a second circle that is inscribed within the pentagon and tangent to the sides internally, called the incircle.
		OM (r1) is the radius of the excircle (the hypoteneuse) of the pentagon.
	www.nexusjournal.com /GA-3.3.html (2317 words)

	Triangle - Wikipedia, the free encyclopedia
		There are three other important circles, the excircles; they lie outside the triangle and touch one side as well as the extensions of the other two.
		A median of a triangle is a straight line through a vertex and the midpoint of the opposite side, and divides the triangle into two equal areas.
		It touches the incircle (at the Feuerbach point) and the three excircles.
	www.search.com /reference/Triangle (2227 words)

	POW_17 (Site not responding. Last check: 2007-10-31)
		If any two sides of a triangle are extended, there is a circle, called an excircle, that is tangent to the two extended sides and the also the non-extended side.
		is the radius of the excircle tangent to side BC with length a.
		In the figure we see that the area of the quadrilateral AMON can be found by adding the areas of right triangles AMO and ANO.
	courses.ncssm.edu /goebel/statecon/Problems/Solutions/Sow_17/Sow_17.htm (204 words)

	Nine point circle (Site not responding. Last check: 2007-10-31)
		If an orthocentric system of four points is given, any three of them define a triangle, and these four triangles all have the same nine point circle.
		The centers of the incircle and excircles of a triangle form an orthocentric system.
		The nine point circle created for that orthocentric system is the circumcircle of the original triangle.
	www.serebella.com /encyclopedia/article-Nine_point_circle.html (727 words)

	MathLinks Math Forums :: View topic - Excircle of APR at AP = excircle of PQB at PQ <==> S is...
		MathLinks Math Forums :: View topic - Excircle of APR at AP = excircle of PQB at PQ <==> S is...
		Excircle of APR at AP = excircle of PQB at PQ <==> S is...
		The condition expressed in excircles is equivalent, in this configuration, to the
	www.mathlinks.ro /Forum/topic-36596.html (253 words)

	Excenter, Excircle, Triangle: College Geometry, SAT Prep - Antonio Gutierrez
		Excenter, Excircle, Triangle: College Geometry, SAT Prep - Antonio Gutierrez
		An excircle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two.
		The center of an excircle is called the excenter, and the radius of the circle is called the exradius.
	agutie.homestead.com /files/problem/excenter_excircle.htm (79 words)

	Use GSP-4 to Explore Circles
		An excircle is tangent to the extensions of two sides of a triangle and also tangent to the third side.
		To begin to locate the point of tangency that will determine the radius of the excircle, construct the line perpendicular to segment BC and passing through point XC.
		Other material and challenges concening excircles were found by searching for "excircles" on the Math Forum.
	mathforum.org /~shelly/Lucent/gsp4_explore_circles.html (845 words)

	HYPERBOLIC GEOMETRY (Site not responding. Last check: 2007-10-31)
		If it exists, the excircle arising from the external bisectors at B and C
		is the excircle opposite A. Its radius is denoted by RA.
		The radius of the incircle is R. The cabrijava applet allows you to experiment in the hyperbolic plane.
	www.maths.gla.ac.uk /~wws/cabripages/hyperbolic/incircles.html (333 words)

	angle bisectors
		(remember S is the semi-perimeter, and b is the side adjacent to this excircle) This could be repeated for any of the three excircles.
		. Another interesting fact about this figure is that the three excircles are all externally tangent to the Nine Point Circle (not shown in the figure), and the incircle is internally tangent to it.
		The radii of the four circles shown are related by a single equation,
	www.pballew.net /Tribis.html (377 words)

	Nagel Point of the Medial Triangle
		But this is the characteristic property of the points of tangency of the excircles and, therefore, of the Nagel point.
		The applet's diagram can be used to illustrate the fact of isotomic conjugacy of the Nagel and Gergonne points.
		However, as we've seen, R is also the point of tangency of the excircle of
	www.cut-the-knot.com /Curriculum/Geometry/MedialNagel.shtml (466 words)

	Math Forum - Ask Dr. Math
		Conclusion: when you multiply O over G with factor -2, you get H. And thus the three points must be on one line.
		Now the Nagel point: The Nagel point is the point of concurrence of the three lines connecting the triangle vertices and the point where the excircle meets the opposite side.
		Consider this line from the A-vertex: / C" / B A'B"C" are the points where the / \ A-excircle meets the sides of ABC.
	mathforum.org /library/drmath/view/55027.html (399 words)

	ENCYCLOPEDIA OF TRIANGLE CENTERS
		Let A'B'C' be the points in which the A-excircle meets BC, the B-excircle meets CA, and the C-excircle meets AB, respectively.
		Feuerbach's famous theorem states that the nine-point circle is tangent to the incircle and the three excircles.
		Let A'B'C' be the touch points of the nine-point circle with the A-, B-, C- excircles, respectively.
	faculty.evansville.edu /ck6/encyclopedia/ETC.html (10355 words)

	The Gateway to Educational Materials - lesson plans, curriculum units and other education resources in the subject ... (Site not responding. Last check: 2007-10-31)
		The lines connecting each vertex of a triangle ABC with the point of tangency between the opposite side and the opposite excircle are concurrent at a point N called the Nagel Point.
		This is a step by step illustration of the semiperimeter, excircles, and incircles theorem.
		This is a step by step illustration of the semiperimeter and excircles theorem.
	io.syr.edu /query.html?col=gemdata&ht=0&qp=&qs=&qc=&pw=100%25&la=en&charset=iso-8859-1&si=0&fs=&qt=&ex=&rq=0&oq=&ct=957688015&ws=0&qm=1&ql=&st=451&nh=25&lk=1&rf=3 (1230 words)

	Homework Assignments Math 330 Fall 2001
		Given triangle ABC, construct the incircle and one excircle.
		Construct the other two lines corresponding to the other two excircles.
		Since this is a construction problem, you cannot use the script we wrote for inversion, because it uses transformations.
	www.uwec.edu /smithaj/Fall2001/330/homework_assignments.htm (603 words)

	Art of Problem Solving Forum
		Also i think a kite is a counter-example to that statement; since a kite has no excircle.
		This is an arrangement-independent version of the well-known fact that a quadrilateral ABCD has an incircle if and only if AB + CD = BC + DA, and of all pendants of this fact related to excircles and concave quadrilaterals.
		Concerning your comment, Peter, one doesn't need imaginary radii, but it's indeed impossible to distinguish between "incircles" and "excircles" in general.
	www.artofproblemsolving.com /Forum/post-23019.html (1239 words)

	Problems for Vol. 99(4), April 1999 issue (Site not responding. Last check: 2007-10-31)
		denote the incircle and the excircle to side BC, respectively.
		, by considering the excircles to sides CA and AB, respectively.
		Note: For two related problems, see the solution of Problem 4153 in the October, 1988 issue, and the solution of Problem 4223 in the January, 1990 issue.
	oregonstate.edu /pubs/ssm/pro_Apr99.html (293 words)

	Aquinas College :: Mathematics
		Just divide the result from #11 by 2 to get semi-circle results.
		The excircle proof is just the same as the incircle proof.
		Hint: the sides of an angle are equidistant from any point on the angle bisector.
	www.aquinas.edu /mathematics/class.html (309 words)

	klein view page
		the latter includes the case of a horocycle as excircle.
		A CabriJava applet is used to show that a hyperbolic triangle may have up to three
		excircles, but may have 0, 1, 2 or 3.
	www.maths.gla.ac.uk /~wws/cabripages/news.html (484 words)

	Art of Problem Solving Forum
		I dont think this is true when ABDF is convex, e.g.
		You can also prove it in an arrangement-independent way (using the angle bisector between two directed lines - the set of all points having equal directed distances to these two lines).
		It is, BTW, a nice exercise on directed lines.
	www.artofproblemsolving.com /Forum/ptopic-6574.html (1240 words)

	[No title]
		7 Jan: A user reported that the excircle constructor in the 2-dim window was not working.
		Indeed, this got damaged when I was enabling the excircle constructor for the new spherical window, because the two windows share a lot of coding.
		Keep me posted on any other items that I might have recently damaged.
	peanut.8m.net /wingeom.html (1273 words)

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