View source for Geometry/Chapter 9/Lesson 1

==Introduction==
This lesson will introduce you to vocabulary about '''circles'''.

==Terminology==
#'''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.
#'''Radius''' is a ''segment'' that showcases the distance from the center outwards to any point in the circle.
#'''Chord''' is a ''segment'' with endpoints on the circle.
#'''Diameter''' is a chord that contains the center point.
#'''Secant''' is a ''line'' that intersects the circle at two points.
#'''Circumference''' is the distance around the circle. Circumference formula: 2πr or πd (r=radius; d=diameter).
#'''Area''' is the number of square units inside of a circle.
#'''Central Angle''' is an ''angle'' in which its vertex is the center point and its two sides are radii. 
#'''Inscribed angle''' is an ''angle'' in which the sides are "chords" and [those chords] share a common endpoint.
#'''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. 
#'''Inscribed polygon''' is where a polygon is "outside" of the circle, in which the sides of the polygon are chords to the circle.
#'''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.
#'''Tangent''' is a line that intersects on one point on the circle.
#'''Point of Tangency''' is the point where a circle and a tangent intersect. 
#'''Congruent circles''' are circles that are congruent because they have congruent radii.
#'''Concentric circles''' have the same center but different radii length.
#'''Interior angle''' is where the angle is inside of the figure (circle); vertex is not in the center.
#'''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 <math>7</math>. 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'''


[[Category:Geometry]]