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Equivalently, an inscribed angle is defined by two chords of the circle sharing an endpoint. The inscribed angle theorem relates the measure of an inscribed angle to that of the central angle intercepting the same arc. The inscribed angle theorem appears as Proposition 20 in Book 3 of Euclid's Elements.
An inscribed angle (examples are the blue and green angles in the figure) is exactly half the corresponding central angle (red). Hence, all inscribed angles that subtend the same arc (pink) are equal. Angles inscribed on the arc (brown) are supplementary. In particular, every inscribed angle that subtends a diameter is a right angle (since the ...
Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid's Elements. [1] It is generally attributed to Thales of Miletus, but it is sometimes attributed to Pythagoras.
Inscribed angle theorem. Thales' theorem, if A, B and C are points on a circle where the line AC is a diameter of the circle, then the angle ∠ABC is a right angle. Alternate segment theorem. Ptolemy's theorem. The Milne-Thomson circle theorem in fluid dynamics. Five circles theorem; Six circles theorem; Seven circles theorem; Gershgorin ...
By the inscribed angle theorem, the central angle subtended by the chord ¯ at the circle's center is twice the angle , i.e. (+). Therefore, the symmetrical pair of red triangles each has the angle α + β {\displaystyle \alpha +\beta } at the center.
Inscribed angle theorem for an ellipse. Like a circle, such an ellipse is determined by three points not on a line. For this family of ellipses, one introduces the following q-analog angle measure, which is not a function of the usual angle measure θ: [16] [17]
Planar angle is an inscribed angle subtending the same arc, so by the inscribed angle theorem has measure . This relationship is preserved for any choice of C {\displaystyle C} ; therefore, the spherical excess of the triangle is constant whenever C {\displaystyle C} remains on the Lexell circle l , {\displaystyle l,} which projects to a line ...
In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle.