1 / 26

Bell work 1

Bell work 1. A. C. Find the measure of Arc ABC, if Arc AB = 3x, Arc BC = (x + 80 º), and __ __ AB  BC. AB = 3x º. BC = ( x + 80 º ). B. AB = 3x º. Bell work 1 Answer. Since, __ __ AB  BC , then AB  BC, thus 3x = x + 80º 2x = 80º x = 40º = AB & BC

cybil
Download Presentation

Bell work 1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Bell work 1 A C Find the measure of Arc ABC, if Arc AB = 3x, Arc BC = (x + 80º), and __ __ AB BC AB = 3xº BC = ( x + 80º ) B

  2. AB = 3xº Bell work 1 Answer Since, __ __ AB BC , then AB  BC, thus 3x = x + 80º 2x = 80º x = 40º = AB & BC Therefore AB + BC = ABC = 240º C A B BC = (x + 80º)

  3. Bell work 2 You are standing at point X. Point X is 10 feet from the center of the circular water tank and 8 feet from point Y. Segment XY is tangent to the circle P at point Y. What is the radius, r, of the circular water tank? Y 8 ft • X r 10 ft • P

  4. Bell work 2 Answer Use the Pythagorean Theorem since segment XY is tangent to circle P at Point Y, then it is perpendicular to the radius, r at point Y. r =6 ft

  5. Unit 3 : Circles: 10.3 Arcs and Chords Objectives: Students will: 1. Use inscribed angles and properties of inscribed angles to solve problems related to circles

  6. Inscribed Angle Intercepted Arc Inscribed Polygons Circumscribed Circles Words for Circles Are there any words/terms that you are unsure of?

  7. INTERCEPTED ARC, AB A B Inscribed Angles Inscribed angle – is an angle whose vertex is on the circle and whose sides contain chords of the circle. INSCRIBED ANGLE Vertex on the circle

  8. INTERCEPTED ARC, AB A B Intercepted Arc Intercepted Arc – is the arc that lies in the interior of the inscribed angle and has endpoints on the angle. INSCRIBED ANGLE Vertex on the circle

  9. (p. 613) Theorem 10. 8 Measure of the Inscribed Angle The measure of an inscribed angle is equal half of the measure of its intercept arc. Central Angle m∕_ ABC = ½ m AC A • CENTER P P B • • C Inscribed angle

  10. Example 1 The measure of the inscribed angle ABC = ½ the measure of the intercepted AC. Central Angle A • Measure of the INTERCEPTED ARC = the measure of the Central Angle AC = 60º B • 30º • 60º m∕_ ABC = ½ mAC = 30º • C

  11. Example 2 Find the measure of the intercepted TU, if the inscribed angle R is a right angle. T • R • • U

  12. Example 2 Answer The measure of the intercepted TU = 180º, if the inscribed angle R is a right angle. T • TU = 180 º R • • U

  13. Example 3 Find the measure of the inscribed angles Q , R ,and S, given that their common intercepted TU = 86º Q T • TU = 86º R • • S U

  14. Example 3 Answers Angles Q, R, and S = ½ their common intercepted arc TU Since their intercepted Arc TU = 86º, then Angle Q = Angle R = Angle S = 43º Q T • TU = 86º R • • S U

  15. (p .614) Theorem 10.9 If two inscribed angles of a circle intercepted the same arc, then the angles are congruent Q T IF∕_ Qand∕_ Sboth intercepted TU,then ∕_ Q∕_ S • • • S U

  16. Inscribed vs. Circumscribed Inscribed polygon – is when all of its vertices lie on the circle and the polygon is inside the circle. The Circle then is circumscribed about the polygon Circumscribed circle – lies on the outside of the inscribed polygon intersecting all the vertices of the polygon.

  17. Inscribed vs. Circumscribed The Circle is circumscribed about the polygon. Circumscribed Circle Inscribed Polygon

  18. (p. 615) Theorem 10.10 If a right triangle is inscribed in a circle, then the hypotenuse is the diameter of the circle. Hypotenuse = Diameter •

  19. (p. 615) Converse of Theorem 10.10 If one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is a right angle. The triangle is inscribed in the circle and one of its sides is the diameter Angle B is a right angle and measures 90º • Diameter = Hypotenuse B

  20. Example Triangle ABC is inscribed in the circle Segment AC = the diameter of the circle. Angle B = 3x. Find the value of x. A • C 3xº B

  21. Answer Since the triangle is inscribed in the circle and one of its sides is the diameter = hypotenuse side, then its opposite angle, Angle B, measures 90º Thus, 3x = 90º x = 30º

  22. (p. 615) Theorem 10.11 A quadrilateral can be inscribed in a circle iff its opposite angles are supplementary. The Quadrilateral WXYZ is inscribed in the circle iff / X + / Z = 180º, and / W + / Y = 180º X Y • • • P • W • Z

  23. Example A quadrilateral WXYZ is inscribed in circle P, if ∕_ X = 103º and ∕_ Y = 115º , Find the measures of ∕_ W = ? and ∕_ Z = ? The Quadrilateral WXYZ is inscribed in the circle iff / X + / Z = 180º, and / W + / Y = 180º X Y • • • 103º 115º P • W • Z

  24. Example From Theorem 10.11 ∕_ W = 180º – 115º = 65º and ∕_ Z = 180º – 103º = 77º The Quadrilteral WXYZ is inscribed in the circle iff / X + / Z = 180º, and / W + / Y = 180º X Y • • • 103º 115º P • W • Z

  25. Home work PWS 10.3 A P. 617 (9 -22) all

  26. Journal Write two things about “Inscribed Angles” or “Inscribed Polygons” related to circles from this lesson.

More Related