Geometry/Chapter 9/Lesson 1

Introduction

This lesson will introduce you to vocabulary about circles.

Terminology

1. Circle is a "simple-closed" shape in which all points are equidistant to the center point of the circle, in which the circle is named by the center (ex: Circle A); coplanar points.
2. Radius is a segment that showcases the distance from the center outwards to any point in the circle.
3. Chord is a segment with endpoints on the circle.
4. Diameter is a chord that contains the center point.
5. Secant is a line that intersects the circle at two points.
6. Circumference is the distance around the circle. Circumference formula: 2πr or πd (r=radius; d=diameter).
7. Area is the number of square units inside of a circle.
8. Central Angle is an angle in which its vertex is the center point and its two sides are radii.
9. Inscribed angle is an angle in which the sides are "chords" and [those chords] share a common endpoint.
10. Arc is a part of the circle's circumference.
    • Minor arc is an arc below 180 degrees.
    • Semicircle is an arc that equals to 180 degrees and contains a diameter.
    • Major arc is an arc above 180 degrees.
    • Intercepted arc is an arc intercepted by segments in a circle.
11. Inscribed polygon is where a polygon is "outside" of the circle, in which the sides of the polygon are chords to the circle.
12. Circumscribed polygon is where the vertices of the polygon do not lie on the circle and the sides [of the polygons] are tangents to the circle.
13. Tangent is a line that intersects on one point on the circle.
14. Point of Tangency is the point where a circle and a tangent intersect.
15. Congruent circles are circles that are congruent because they have congruent radii.
16. Concentric circles have the same center but different radii length.
17. Interior angle is where the angle is inside of the figure (circle); vertex is not in the center.
18. Exterior angle is where the angle is outside of the figure (circle). The sides are either tangents or secants.

Tips/Notes

• π = 3.14 (pi)
• All radii are congruent.
• Exact circumference: π
  • If a problem asks for the exact circumference, you include π.

Finding circumference

If you know the radius, finding the circumference is simple. Use 2πr or πd to find it!

• Q: Radius is $7$. Find the circumference.
  • A: 2πr --> 2π(7) --> 14π (if pi has to be left in the answer) or 43.98.

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• Q: Find d and r to the nearest tenth if C = 196.7.
  • A: Plug in your inputs into the circumference formula.
    • C = πd
    • (196.7) = πd
    • (196.7)/π = πd/π
    • 62.61 = d

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• • • r=1/2d
    • r=1/2(62.61)
    • r= 31.31