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10.5 Other Angles

10.5 Other Angles. In a Circle. Vertex on the circle. When the vertex of the angle is on the circle, the measure of the angle is half the intercepted arc. Formed by two chords Formed by chord and tangent. Chord/Tangent. Two Chords. What are the missing measures?. Angles inside the Circle.

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10.5 Other Angles

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  1. 10.5 Other Angles In a Circle

  2. Vertex on the circle • When the vertex of the angle is on the circle, the measure of the angle is half the intercepted arc. • Formed by two chords • Formed by chord and tangent

  3. Chord/Tangent Two Chords What are the missing measures?

  4. Angles inside the Circle • If two chords intersect inside the circle, then the angle is the average of the intercepted arcs of the vertical angles. (half the sum) 80 ° What is the measure of Angle 1? ½( 80 + 30) = 55 ° 1 30°

  5. Angles Outside the Circle • If a tangent/ tangent, secant/secant or tangent/secant intersect outside a circle the angle formed is half the difference of the intercepted arcs. a a a b b b Tangent/secant Secant/secant Tangent/tangent Angle = ½ (a-b)

  6. = m TSR m1 12 (210o) (98o) 2 = for Example 1 GUIDED PRACTICE Find the indicated measure. SOLUTION SOLUTION = 105o = 196o

  7. The chords ACand CDintersect inside the circle. = 12 12 78o (yo + 95o) = 61 = y GUIDED PRACTICE Find the value of the variable. SOLUTION (mAB + mCD) 78° Use Theorem 10.12. Substitute. 156 = y +95 Simplify.

  8. SOLUTION The tangent JFand the secant JGintersect outside the circle. (mFG – mKH) m FJG = 12 12 30o (ao – 44o) = a = 104 GUIDED PRACTICE Find the value of the variable. Use Theorem 10.13. Substitute. 60 = a - 44 Simplify.

  9. (mTUR – mTR) m TQR 12 12 = 73.7o [(xo) –(360 –x)o] xo 253.7 CP GUIDED PRACTICE Find the value of the variable. SOLUTION Congruent triangles (HL) Trig using 3-4-5 Use Theorem 10.13. Substitute. 147.4 = x – 360 + x Solve for x. 507.4 = 2x

  10. Review of all angles with circles • Central angle = the intercepted arc. • Vertex on circle = half the intercepted arc. (chords sharing common endpoint or a chord and a tangent intersecting on circle.) • Vertex inside circle = half the sum • Vertex outside circle = half the difference

  11. On –half arc Central = Inside –half sum Outside---half difference

  12. Geometry • Page 683 (1-6, 9-14,16-18,22-25,34-39)

  13. Sophomore Math • Page 683 (1-16, 22)

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