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Warm up…

Warm up…. Page 543 quiz #’s 1 – 6, 9, 10. 10-4 Inscribed Angles. Inscribed Angles. If an angle is inscribed in a circle, then the measure of the angle equals ½ the measure of the intercepted arc The measure of the intercepted arc is 2 times the measure of the inscribed angle. B. A. D. C.

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Warm up…

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  1. Warm up… • Page 543 quiz #’s 1 – 6, 9, 10

  2. 10-4 Inscribed Angles

  3. Inscribed Angles • If an angle is inscribed in a circle, then the measure of the angle equals ½ the measure of the intercepted arc • The measure of the intercepted arc is 2 times the measure of the inscribed angle B A D C

  4. Intercepting the same arc • If 2 inscribed angles intercept congruent arcs or the same arc then the angles are congruent A B B A C F D C D E

  5. Angles of inscribed polygons • If an inscribed angle intercepts a semicircle, the angle is a right angle A D B C ADC is a semicircle, so m<ABC = 90°

  6. Example 1: • mWX=20, mXY=40, mUZ=108 and mUW=mYZ. Find the measures of the numbered angles. W X 3 Y 4 5 F 2 U Z 1 T

  7. Example 2: • Triangles TVU and TSU are inscribed in circle P, m<2 = x+9 and m<4 =2x+6, • Find the measure of the numbered angles U V 3 4 S P 1 2 T

  8. Inscribed Quadrilaterals • If a quadrilateral is inscribed in a circle then its opposite angles are supplementary

  9. 10-6 Secants, Tangents and Angle Measure

  10. Secants • A line that intersects a circle in exactly 2 points • When 2 secant lines intersect in the interior of a circle the measure of an angle formed is ½ the sum of the measures of the intercepted arcs and its vertical angle A D m<1 = ½(mAC + mBD) m<2 = ½(mAD + mBC) 2 1 B C

  11. Secant and Tangent • If a secant and a tangent intersect at a point of tangency, then the measure of each angle formed is ½ the measure of the intercepted arc • Example: Find m<RPS if mPT =114 and mTS = 136 R P Q S 114° T 136°

  12. Intersection outside a circle D • Two secants – m<A = ½(mDE – mBC) • Secant-tangent – m<A=1/2(mDC – mBC) • Two tangents – m<A=1/2(mBDC – mBC) B A C E D B A C B D A C

  13. Examples: Find x 40° 6x 55° 141° x 62°

  14. Assignment: • Page 549 #13-16 all • Page 564 # 13-27 odd

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