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Catégorie :Category: nCreator TI-Nspire
Auteur Author: cheeseburgqr
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 1.79 Ko KB
Mis en ligne Uploaded: 25/08/2025 - 10:48:07
Uploadeur Uploader: cheeseburgqr (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : https://tipla.net/a4826285
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 1.79 Ko KB
Mis en ligne Uploaded: 25/08/2025 - 10:48:07
Uploadeur Uploader: cheeseburgqr (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : https://tipla.net/a4826285
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
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1) Angle at the centre is twice the angle at thecircumference Theorem. For a circle with centre and distinct points on the circle (with on arc ), Proof. Join . Since (radii), triangles and are isosceles. Let Then So At the circumference, Thus 2) Angle in a semicircle is a right angle Theorem. If is a diameter and lies on the circle, then . Proof. . By Theorem 1: 3) Angles in the same segment are equal Theorem. If lie on a circle with on the same arc , then Proof. By Theorem 1: So . 4) Opposite angles of a cyclic quadrilateral Theorem. If is cyclic, then Proof. Angles subtend supplementary arcs: But arcs . So Same for . 5) Radius  tangent Theorem. If tangent touches circle at and centre is , then . Proof. Take any other point on tangent line . Then since only lies on circle. The shortest distance from to line is the perpendicular, so is perpendicular. 6) Alternate segment theorem(tangentchord) Theorem. If tangent at and chord are drawn, then for any point on the opposite arc. Proof. Let . By Theorem 1: In , isosceles with , Now angle between tangent at and chord is Sotangentchord angle = inscribed angle. Made with nCreator - tiplanet.org
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Compatible OS 3.0 et ultérieurs.
<<
1) Angle at the centre is twice the angle at thecircumference Theorem. For a circle with centre and distinct points on the circle (with on arc ), Proof. Join . Since (radii), triangles and are isosceles. Let Then So At the circumference, Thus 2) Angle in a semicircle is a right angle Theorem. If is a diameter and lies on the circle, then . Proof. . By Theorem 1: 3) Angles in the same segment are equal Theorem. If lie on a circle with on the same arc , then Proof. By Theorem 1: So . 4) Opposite angles of a cyclic quadrilateral Theorem. If is cyclic, then Proof. Angles subtend supplementary arcs: But arcs . So Same for . 5) Radius  tangent Theorem. If tangent touches circle at and centre is , then . Proof. Take any other point on tangent line . Then since only lies on circle. The shortest distance from to line is the perpendicular, so is perpendicular. 6) Alternate segment theorem(tangentchord) Theorem. If tangent at and chord are drawn, then for any point on the opposite arc. Proof. Let . By Theorem 1: In , isosceles with , Now angle between tangent at and chord is Sotangentchord angle = inscribed angle. Made with nCreator - tiplanet.org
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