1. GEOMETRY: Chapter 10
10.1: Tangents to Circles

2. A chord is a segment whose endpoints are on a circle.
A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. A circle with center P can be written P. A segment whose endpoints are the center of any point on the circle is a radius.
A chord is a segment whose
endpoints are on a circle.
A diameter is a chord that
contains the center of a circle.
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3. A secant is a line that intersects a circle in two points
A secant is a line that intersects a circle in two points. A tangent is a line in the plane of a circle that intersects the circle in exactly one point, the point of tangency. The tangent ray and the tangent segment are also called tangents.
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4. Ex.1:
Tell whether the line or segment is best described as a radius, chord, diameter, secant, or tangent of circle C.
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5. Ex.1:
Tell whether the line or segment is best described as a radius, chord, diameter, secant, or tangent of circle C.
Answer: a) radius; b) secant; c) diameter; d) tangent
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6. Ex.2: Use the diagram to find the given lengths.
Radius of circle B
Diameter of circle A
Radius of circle A
Diameter of circle B
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7. Ex.2: Use the diagram to find the given lengths.
Radius of circle B
Diameter of circle A
Radius of circle A
Diameter of circle B
Answer: a) 3 units; b) 4 units; c) 2 units; d) 6 units
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8. COPLANAR CIRCLES—Two circles can intersect in two points, one point, or two points. Coplanar circles that intersect in one point are called tangent circles. Coplanar circles that have a common center are called concentric.
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9. Common Tangents—A line, ray, or segment that is tangent to two coplanar circles is called a common tangent.
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10. Ex.3: Tell how many common tangents the circles have and draw them.
Answer: a. 2 common tangents; b. 4 common; c. 3 common tangents
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11. Ex.3: Tell how many common tangents the circles have and draw them.
Answer: a. 2 common tangents; b. 4 common; c. 3 common tangents
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12. Theorem 10.1and 10.2:
In a plane, a line is tangent to a circle if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle.
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13. Ex.4:
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14. Ex.4:
Answer:No =4225, but 672=4489
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15. Ex.5:
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16. Ex.5:
Answer: 14 cm
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17. Tangent Segments from a common external point are congruent.
Theorem 10.3:
Tangent Segments from a common external point are congruent.
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18. Ex.6:
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19. Ex.6:
Answer: 5.5
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20. 10.1, p. 599, #6-29 all