Lesson 10.6 – Secants, Tangents, and Angle Measure Standards G.6.2, G.6.5

Definitions Unlike diameters and chords, tangents and secants are lines, not line segments. A tangent is a line which intersects a circle only once. A secant is a line which intersects a circle twice.

Angle Measures When a combination of secants and tangents are drawn in a circle, they intersect in one of three ways: Inside the Circle Outside the Circle On the Circle

Intersection Inside Circle Angle measures: Add the two opposite arc measures together and divide by 2. Arc 2 <1 <2 A B C Arc 1 Arc 3 D Arc 4

Example 1 Find m<1 B Find m<2 <2 <1 A 1700 30 + 40 = 70/2 = 350 Find m<2 170 + 120 2 = 290/2 400 300 = 1450 1200

Intersection Outside Circle Angle measures: Large arc – small arc divided by 2 A B <1 D C

Example 2 Find x 141-62 2 = 79/2 1410 x0 620 = 39.5

Intersection on the Circle Angle measures: Half of the intercepted arc (same as inscribed angle!) A <1 B m<1 = arc ABC 2 C

Example 3 Find m<1 300 2 <1 = 1500 3000

Example 4 Arc AB = 600 Arc BC = 500 Arc CD = 1300 Arc AD = m<1 = <4 600 1200 B Arc AD = m<1 = m<2 = m<3 = m<4 = 1200 <2 850 <1 <3 500 950 950 D C 550 1300

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