9-1 Basic Terms associated with Circles and Spheres



9-1 Basic Terms associated with Circles and Spheres

Circle __________________________________________________________________

Given Point = __________________ Given distance = _____________________

Radius__________________________________________________________________

Chord____________________________________________________________________

Secant___________________________________________________________________

Diameter__________________________________________________________________

Tangent___________________________________________________________________

Point of Tangency___________________________________________________________

Sphere____________________________________________________________________

Label Accordingly:

Congruent circles or spheres__________________________________________________

Concentric Circles___________________________________________________________

Concentric Spheres__________________________________________________________

Inscribed in a circle/circumscribed about the polygon________________________________ _______________________________________



SKETCHPAD

9-2 Tangents POWERPOINT

Theorem 9-1 If a line is tangent to a circle , then the line is __________________________

_________________________________.

Corollary: Tangents to a circle from a point are __________________________

Theorem 9-2 If a line in the plane of a circle is perpendicular to a radius at its outer endpoint, then the line is ________________________.

Inscribed in the polygon/circumscribed about the circle:

Common Tangent ___________________________________________________

Common Internal Tangent

Common External Tangent

Tangent circles ________________________________________________________

Draw the tangent line for each drawing

Name a line that satisfies the given description.

1. Tangent to ( P but not to ( O. _______

2. Common external tangent to ( O and ( P. _______

3. Common internal tangent to ( O and ( P. _______

4. Circles A, B, C are tangent . AB = 7, AC = 5 CB = 9

Find the radii of the circles.

5. Find the radius of the circle inscribed in a 3-4-5 triangle.

PP CONCLUSION

6) Circles O and P have radii 18 and 8 respectively. [pic] is tangent to both circles.

Find AB…………….Hint: connect centers. Find a rt.

9-3 Arcs and Central Angles

Central Angle ________________________________________________________

Arc ________________________________________________________________

Measure of a minor arc = ______________

Measure of a major arc = __________ - ______________

Adjacent arcs ____________________

Measure of a semicircle = ___________________

Postulate 16 Arc Addition Postulate: The measure of the arc formed by two adjacent arcs is _________________________________________.

That is, arcs are additive. Just like with angles, to differentiate an arc from its measure, an “m” must be included in front of the arc.

Congruent arcs _______________________________

Theorem 9-3 In the same circle or _________________, two minor arcs are _____________ if _________________________________.

1. Name 2. Give the measure of each angle or arc:

a) two minor arcs a) AC

b) two major arcs b) m(WOT

c) a semicircle c) XYT

d) an acute central angle

e) two congruent arcs

3. Find the measure of (1 (the central angle)

a) b)

c) d)

4. Find the measure of each arc:

a) AB b) BC c) CD d) DE e) EA

5) a) If [pic], AO = 10, find ................
................

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