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Topic: Central angle

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  Angle - Wikipedia, the free encyclopedia
Angles provide a means of expressing the difference in slope between two rays meeting at a vertex without the need to explicitly define the slopes of the two rays.
Since the circumference of a circle is proportional to its radius, and an arc in an angle is a fixed fraction of the circumference, the measure of the angle is independent of the size of the circle.
The angle between a line and a curve (mixed angle) or between two intersecting curves (curvilinear angle) is defined to be the angle between the tangents at the point of intersection.
en.wikipedia.org /wiki/Angle   (1874 words)

 Encyclopedia :: encyclopedia : Angle   (Site not responding. Last check: 2007-10-27)
The degree measure of the angle is the length of the arc, divided by the circumference of the circle, and multiplied by 360.
This angle is equal to π/2 radians minus the angle between the intersecting line and the line that goes through the point of intersection and is perpendicular to the plane.
The modern format of angle used to indicate longitude or latitude is hemisphere degree minute.decimal, where there are 60 minutes in a degree, for instance N 51 23.438 or E 090 58.928.
www.hallencyclopedia.com /Angle   (1424 words)

 Circle - Wikipedia, the free encyclopedia
If a central angle and an inscribed angle of a circle are subtended by the same chord and on the same side of the chord, then the central angle is twice the inscribed angle.
For a cyclic quadrilateral, the exterior angle is equal to the interior opposite angle.
The angle between a tangent and chord is equal to the subtended angle on the opposite side of the chord.
en.wikipedia.org /wiki/Circle   (1408 words)

 Inscribed and Central Angles in a Circle
In this case, the central angle BOC plays the role of the external angle of the triangle, such that it equals the sum of the two base angles of the triangle.
This angle is still equal to one half of the central angle subtended by the chord.
The relationship between the arcs and inscribed angles that we have described underscores a simple fact that circular arcs are two arcs of two circles loci of points from a segment is seen under a fixed angle.
www.cut-the-knot.org /Curriculum/Geometry/InscribedAngle.shtml   (571 words)

 Central angle - Wikipedia, the free encyclopedia
Angle AOB forms a central angle of circle O
On a sphere or ellipsoid, the central angle is delineated along a great circle.
Central Angle of an Arc definition With interactive animation
en.wikipedia.org /wiki/Central_angle   (194 words)

Appendix 1d   (Site not responding. Last check: 2007-10-27)
Draw the diagonal of the square, which is also a chord of the of the right central angle, producing an isosceles right triangle equal to the one previously referred to as triangle #1.
Putting a central angle into a standard position in this manner, it should be clear that the base angles of its supplementary isosceles triangle are always equal to half the given central angle.
The shift in the angular reference of measure to the central angle also maintains a more comparable measure between the systems of measure represented by degrees and by radians, which is a reflection of the trigonometric:geometric relation.
www.trisector.org /Append1d.html   (2080 words)

 Arc length -- Topics in trigonometry
At that central angle, the arc is four fifths of the radius.
In a circle whose radius is 10 cm, a central angle θ intercepts an arc of 8 cm.
Note that an angle of 1 radian is a central angle whose subtending arc is equal in length to the radius.
www.themathpage.com /aTrig/arc-length.htm   (841 words)

 SparkNotes: SAT Math Level 2: Circles
An angle whose vertex is the center of the circle is called a central angle.
The degree of the circle (the slice of pie) cut by a central angle is equal to the measure of the angle.
A sector of a circle is the area enclosed by a central angle and the circle itself.
www.sparknotes.com /testprep/books/sat2/math2c/chapter6section4.rhtml   (989 words)

 Circles - angles formed by radii, chords, tangents, secants
A central angle is an angle formed by two intersecting radii such that its vertex is at the center of the circle.
An inscribed angle is an angle with its vertex "on" the circle, formed by two intersecting chords.
At the point of intersection, two sets of vertical angles can be seen in the corners of the X that is formed on the picture.
regentsprep.org /regents/mathb/5A1/CircleAngles.htm   (365 words)

 Welcome to Math Central   (Site not responding. Last check: 2007-10-27)
the angle formed at the centre of a circle by the intersection of two radii.
an angle at the centre of the polygon.
Corresponding angles are congruent if the triangles are similar or congruent.
mathcentral.uregina.ca /RR/glossary/middle/glossaryc.html   (441 words)

 angle - Wiktionary
In the case of a plane angle, this is the ratio (or proportional to the ratio) of the arc length to the radius of a section of a circle cut by the two rays, centered at their common point.
In the case of a solid angle, this is the ratio of the surface area to the square of the radius of the section of a sphere.
The angle between lines A and B is π/4 radians, or 45 degrees.
en.wiktionary.org /wiki/angle   (271 words)

 unit04-sect03-les01-lessonb   (Site not responding. Last check: 2007-10-27)
A central angle is an angle with vertex at the centre.
By definition, the measure of an arc is equal to the measure of its central angle.
because they both subtend the same central angle at O. However, it is fairly obvious that the distance from H to G measured along the arc is not the same as the distance from K to J measured along the arc.
www.cdli.ca /courses/math3204/unit04/section03/lesson01/3-lesson-b.htm   (275 words)

 Cool math .com - Polygons - properties, interior angles, triangles, quadrilaterals, pentagons, hexagons, heptagons, ...
The sum of the angles of a triangle is 180 degrees.
The measure of the central angles of an equilateral triangle:
So, the measure of the central angle of a regular pentagon is 72 degrees.
www.coolmath.com /reference/polygons.html   (1530 words)

 Conjectures in Geometry: Inscribed Angles   (Site not responding. Last check: 2007-10-27)
We define the arc angle to be the measure of the central angle which intercepts it.
Conjecture (Inscribed Angles Conjecture I): In a circle, the measure of an inscribed angle is half the measure of the central angle with the same intercepted arc..
Proof: The intercepted arc for an angle inscribed in a semi-circle is 180 degrees.
www.geom.uiuc.edu /~dwiggins/conj44.html   (392 words)

 Sectors and arcs   (Site not responding. Last check: 2007-10-27)
If the central angle of a sector of a circle is alpha then the area of the sector is the same as the area of any other sector with central angle alpha, regardless of where the sector sits in the circle.
A similar arguent is valid for the length of an arc.
The measure of the central angle is a fraction of 360
mathcentral.uregina.ca /QQ/database/QQ.09.05/wael1.html   (290 words)

 Going in Circles
The bisector of the central angle of a chord perpendicularly bisects the chord.
An inscribed angle is half the measure of the central angle intercepting the same arc.
The measure of an angle formed by a tangent and a chord is half the measure of its intercepted arc.
www.andrews.edu /~calkins/math/webtexts/geom14.htm   (1159 words)

 Math Forum - Ask Dr. Math   (Site not responding. Last check: 2007-10-27)
Geometry Proof - The Inscribed Angle is 1/2 of the Central Angle
The grade 9 math book describes the relationship between a central angle and an inscribed angle (the inscribed angle is 1/2 the central angle).
Using the nature of these triangles, and remembering the fact that the angles in all triangles sum to 180 degrees, you should be able to find your proof.
mathforum.org /library/drmath/view/54803.html   (253 words)

 Central and Inscribed Angles   (Site not responding. Last check: 2007-10-27)
The angle is proportional to the area enclosed by the angle, which is proportional to the circular arc cut by the angle.
In other words, doubling the angle doubles the size of the piece of pie, and doubles the amount of crust at the edge.
Once again the inscribed angle is half the central angle.
www.mathreference.com /geo,ins.html   (241 words)

 All Elementary Mathematics - Study Guide - Geometry - Geometrical locus. Circle and circumference...
A length of arc of a circle is proportional to its radius r and the corresponding central angle
So, a radian measure of any angle is a ratio of a length of an arc, drawn by an arbitrary radius and concluded between the sides of this angle, to the radius of the arc.
As a central angle contains the same quantity of degrees, as its arc (AmC, Fig.45), then any inscribed angle is measured by a half of an arc, which is based on (AmC in our case).
www.bymath.com /studyguide/geo/sec/geo10.htm   (1116 words)

angere, to compress into a bend or to strangle, and the Greek ἀγκύλος (angulοs) crooked, curved; both connected with the Aryan or Indo-European root ank-, to bend) is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.
This is also roughly subdivided into the mil, which has several definitions in practice.
To the ratio there correspond two angles in the geometric range 0 < θ < 2π, since
www.brainyencyclopedia.com /encyclopedia/a/an/angle.html   (1444 words)

 Math Forum - Ask Dr. Math   (Site not responding. Last check: 2007-10-27)
Date: 07/29/97 at 11:38:04 From: Tawny Woods Subject: Trigonometry Find the degree measure, to the nearest tenth, of a central angle whose intercepted arc measures 21 cm.
Now we want to find the central angle that is the same fraction of 360.
To find this, call the measure of our central angle A. A/360 will tell us what fraction A is of the total anglular measure.
mathforum.org /library/drmath/view/54032.html   (384 words)

 [No title]
ÈÈÈÈÈÈÈÈž      $ô ~ÄHÈÈÈÈÈÄîHHÈÈÈîîîÈHÈHÈž\tHHHHÈžîÐî¾:h,HHžÈ´ ¦{«½ÆÀŒŒÞ” Section 10.3: Central Angles and Arcs Lesson: This section is a compilation of vocabulary, a postulate, and a theorem.
This is called the central angle of the circle.
Cut a piece of pipe cleaner, and tape it to denote the central angle of the circle.
filebox.vt.edu /users/megeorg3/GEOM10.3.doc   (186 words)

 SparkNotes: SAT Math Level 1: Circles
Since angle c is an inscribed angle, arc AB must be 120º.
where n is the measure of the central angle which forms the boundary of the sector, and r is the radius.
The sector is bounded by a 70º central angle in a circle whose radius is 6.
www.sparknotes.com /testprep/books/sat2/math1c/chapter6section4.rhtml   (1229 words)

 Activities: Quadrilateral Sum   (Site not responding. Last check: 2007-10-27)
Measure both the inscribed angle, the central angle, and the Arc Measure.
Note the relationship between the measures of the central and inscribed angles as you move the points.
Use a protractor to measure the inscribed and central angles.
www.geom.uiuc.edu /~dwiggins/act44.html   (322 words)

 [No title]
Create the central angle which has the same intercepted arc ( EMBED Equation.DSMT4 ) as your inscribed angle ( EMBED Equation.DSMT4 ).
Use a protractor to measure your inscribed angle and your central angle.
Inscribed Angle:  EMBED Equation.DSMT4 = _________ Central Angle:  EMBED Equation.DSMT4 = _________ 4.
filebox.vt.edu /a/amook/InscribedAngle.doc   (259 words)

 90 degree angle? - Badminton Central Discussion Forums
I was always told to make a right angle or 90 degree angle when preparing for an overhead stroke.
I myself found that power shots such as smashing and clearing are easier with the arm bent nearer to the bicep, however finesse shots such as drops are easier with the 90 degree bent elbow.
gade, are the ones who have their arm at a 90 degree angle.
www.badmintoncentral.com /vb/showthread.php?t=29444   (1095 words)

 central angle definition - Dictionary - MSN Encarta
central angle definition - Dictionary - MSN Encarta
Search for "central angle" in all of MSN Encarta
angle at center of circle: an angle formed in the center of a circle by the meeting of two radii
encarta.msn.com /dictionary_1861687336/central_angle.html   (75 words)

 Central Tools / Central Lighting Angle Lite - 13Watt Fluorescent Work Lite, 25 Ft. Cord - SHOP.COM
Central Tools / Central Lighting Angle Lite - 13watt Fluorescent Work Lite, 25 Ft. Cord
Unique impact and solvent resistant construction patented angle style patented rough service bulb for superior impact protection floating socket for additional bulb protection superior cord life and flexibility with oil and water resistant 18/2 gauge...
All other designated trademarks, copyrights and brands are the property of their respective owners.
www.shop.com /op/aprod-p21056282   (229 words)

 Question Corner -- Angle Between Vertices of a Tetrahedron
Given a regular tetrahedral with a point in the center, find the angle formed from this center point to two corners (next to each other) in the tetrahedral.
In chemistry terms you are actually proving that the the electrons in a tetrahedral shaped molecule are 109.5 degrees apart.
Our goal here is to help you understand mathematical concepts (especially ones that go beyond the standard curriculum), so we would prefer you to ask "Here is a question I have been given, and I would like to understand better how I should go apart tackling such-and-such a part of it.
www.math.toronto.edu /mathnet/questionCorner/tetangle.html   (332 words)

 Stars   (Site not responding. Last check: 2007-10-27)
The central angle (blue) in the central triangle ABC of the regular pentagon is 360°/5 = 72°.
The interior angle of the pentagon is 108°.
Assuming that the small pentagon inside the pentagram also is regular, the marked orange angle is 108°.
www.mathematische-basteleien.de /stars.htm   (1217 words)

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