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10.3 Inscribed angles

10.3 Inscribed angles. Pg 613. Definitions. Inscribed angle- an  whose vertex is on a circle and whose sides contain chords of the circle. Intercepted arc- the arc that lies in the interior of the inscribed angle and has its endpts on the angle. B. BCD. . BD. (. A. . C. D.

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10.3 Inscribed angles

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  1. 10.3 Inscribed angles Pg 613

  2. Definitions • Inscribed angle- an  whose vertex is on a circle and whose sides contain chords of the circle. • Intercepted arc- the arc that lies in the interior of the inscribed angle and has its endpts on the angle B BCD  BD ( A  C D

  3. Thm 10.8measure of an inscribed  • If an  is inscribed in a circle, then its measure is ½ the measure of its intercepted arc. mBAC= ½ m BC B A C (

  4. Example B ( m AED= ? 180o D C A E

  5. Example A mABD = ? 98o 196o C B D

  6. Example x = ? 70 = ½ 7x Or 7x = 140 B 70o A x=20 C 7xo ( m AD = ? 140o D

  7. Thm 10.9 • If two inscribed angles of a circle intercept the same arc, then the s are @. W Y X C W  Y Z

  8. Inscribed Polygon ABCD is inscribed in the circle. • Polygon with ALL vertices on a circle. Circumscribed Circle – the circle around the inscribed polygon. B A C D

  9. Thm 10.10 • If a rt. Δ is inscribed in a circle, then the hypotenuse is a diameter of the circle. • If one side of an inscribed Δ is a diameter of the circle, then the Δ is a rt. Δ & the  opposite the diameter is the rt. . C If AC is a diameter, then ΔABC is a rt. Δ AND B is the rt. . B AC is a diameter. A

  10. Ex: find x. P PQ is a diameter,  R is a rt. . 3x = 900 x = 30 3xo R C Q

  11. Thm 10.11 • A quadrilateral can be inscribed in a circle iff its opposite s are supplementary. A mA + mC = 180o mB +mD = 180o D B So, can a rectangle be inscribed in a circle? Yes, because its opposite s are supplementary. C

  12. Ex: x=? and y=? 85 + x = 180 x = 95 80 + y = 180 y = 100 yo xo 85o 80o

  13. 4x+y=18 y=18-4x Ex: x=? & y=? ** Think back to Algebra! 40x+10y=180 22x+19y=180 22x+19(18-4x)=180 22x+342-76x=180 342-54x=180 -54x=-162 x=3 y=18-4(3) y=18-12 y=6 19y 10y 22x 40x

  14. Assignment

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