Geometry 9 1 An Introduction to Circles Please

Geometry 9. 1 An Introduction to Circles

Please turn to your vocab page. Try to draw each vocab word in the boxes after you hear the definition but before you see the picture.

Circle • The set of all points in a plane distance from a given point. . 3 P P is the center of the circle. The circle is the set of all points in the plane of the screen 3 away from P.

Radius Plural is radii • A segment that joins the cente circle to any point on the circle s ra u di . P

Chord • A segment whose endpoints li. P cho rd

Diameter • A chord that passes through th of the circle. twice as long The diameter is _____ as the radius. . diameter P

Secant • A line that contains a chord of SE NT A C . P

Tangent • A line in the plane of a circle t intersects the circle in exactly o nt ge n Ta . Point of tangency . P

• Try #1 -9

From the Packet, Name: 1) The center: A F E B A D C

Name: 2) Two diameters: DB and FC F E B A D C

Name: 3) A point of tangency: F D E B A D C

Name: 4) Four radii: F E AB B A D and AF and AC and AD C

Name: 5) A tangent: ED F E B A D C

Name: 6) A secant: FC F E B A D C

Name: 7) Six chords: E FB and DF and BC F B A D and DC and DB FC C

8) Why is AC not a. Chord of A: F E B A D A chord is a segment with both endpoints on the circle. AC has only one endpoint on the circle. C

9) Why is BD not a. Chord of A: F E D A chord is a segment not a line. B A C

Please turn back to your vocab page. Try to draw each vocab word in the boxes after you hear the definition but before you see the picture.

Sphere • Sphere: The set of all points in space given distance from any given point is a sphere. • Many of the terms used with circles are also used with spheres. • For example, sphere X has a… center: radii: chords: G diameter: F H secants: tangent: L I X point of tangency: K J

Congruent Circles congruent circles/spheres Circles (or spheres) are congruent if they have congruent radii. 4 4

Concentric Circles concentric circles: Circles that lie in the same plane and have the same center are concentric spheres: Concentric spheres have the same center.

Inscribed Polygon • A polygon is inscribed in a circle if each vertex of the polygon lies on the circle. • A circle is circumscribed about a polygon if each vertex of the polygon lies on the circle. The polygon is inscribed in the circle. Thus, the circle is circumscribed about the polygon. These two sentences have the same meaning.

Try # 10 -13. Screen up!!

In sphere A, draw: 10. a diameter, 11. a chord, 12. a tangent, 13. a secant, 14. Draw two concentric circles. Draw a tangent to one of the circles. Is it tangent to the other circle? 15. Draw a large circle. Inscribe an isosceles triangle in the circle. 16. Draw a rectangle. Circumscribe a circle about the rectangle. A

F In sphere A, draw: 10. a diameter, BC 11. a chord, DE 12. a tangent, CF 13. a secant, DG A B C E D G

• 14. Draw two concentric circles. Draw a tangent to one of the circles. Is it tangent to the other circle? No. • 15. Draw a large circle. Inscribe an isosceles triangle in the circle. • 16. Draw a rectangle. Circumscribe a circle about the rectangle.

Find the value of x. O 6 3 6 60 90 3√ 3 30 x = 6√ 3 6 3√ 3 x 3√ 3 B

Find the value of x. O is the center of each circle. 17. x 18. 8 60 O x O 3 4 4 20. 19. x O 4 45 x x 10 O

Find the value of x. O is the center of each circle. 17. 18. 8 x=5 O x x=8 x 60 O 3 4 19. 20. x O x = 4√ 2 4 45 x 10 O x x = 5√ 2

HW • P. 330 -331 CE 1 -11 WE 1 -15