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.
 * 11) *Minor arc is an arc below 180 degrees.
 * 12) *Semicircle is an arc that equals to 180 degrees and contains a diameter.
 * 13) *Major arc is an arc above 180 degrees.
 * 14) *Intercepted arc is an arc intercepted by segments in a circle.
 * 15) Inscribed polygon is where a polygon is "outside" of the circle, in which the sides of the polygon are chords to the circle.
 * 16) 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.
 * 17) Tangent is a line that intersects on one point on the circle.
 * 18) Point of Tangency is the point where a circle and a tangent intersect.
 * 19) Congruent circles are circles that are congruent because they have congruent radii.
 * 20) Concentric circles have the same center but different radii length.
 * 21) Interior angle is where the angle is inside of the figure (circle); vertex is not in the center.
 * 22) Exterior angle is where the angle is outside of the figure (circle). The sides are either tangents or secants.

Tips/Notes
If you know the radius, finding the circumference is simple. Use 2πr or πd to find it! - --
 * π = 3.14 (pi)
 * All radii are congruent.
 * Exact circumference: π
 * If a problem asks for the exact circumference, you include π.
 * Finding circumference
 * Q: Radius is $$7$$. Find the circumference.
 * A: 2πr --> 2π(7) --> 14π (if pi has to be left in the answer) or 43.98.
 * 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
 * r=1/2d
 * r=1/2(62.61)
 * r= 31.31