# Geometry/Chapter 9/Lesson 1

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## Introduction[edit]

This lesson will introduce you to vocabulary about **circles**.

## Terminology[edit]

**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[edit]

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

- If a problem asks for the exact circumference, you include

- Finding circumference

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

**Q**: Radius is . 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**