G.C.A.2STUDENT NOTES & PRACTICE WS #2 – geometrycommoncore.com1

/ Arc – An Arc is a piece or portion of the circumference of a circle. Arcs are classified into two types, major and minor arcs. Major arcs have a value greater than 180 and minor arcs have a value less than 180. These arcs also have naming conventions; minor arcs are named using its two endpoints, such as or while major arcs include a third point between its two endpoints to help distinguish the direction and size of the arc, such as or .
Semi-Circle – You might have noticed that major and minor arcs were either bigger or smaller than 180. So how do we refer to the arc when it is exactly 180? It is called a semi-circle. A semi-circle is an arc that is exactly half of the circle and has an arc measure of 180. There is no distinction as to whether semi-circles should be written as a major or minor arc - actually either is acceptable, such as , , . The reason you might use three letters is to help distinguish which half of the circle you are referring to. /
Major Arc, / Minor Arc, / Semi-Circle, / Arc Addition
Greater than 180 / Less than 180 / Equal to 180 /

Arc Length (Distance) & Arc Angle (Angle Measure)

Arcs have two ways to measure them - their length and their angle measure. Arc length refers to the physical distance along the arc from one end to the other. Arc length is a portion or percentage of the circumference distance. The arc angle or arc measure refers to the portion or percentage of the circles angle sum. When we refer to the measurement of an arc (its angle measure) we place a lowercase italic m in front of the arc name, . The m denotes the measure of the arc -- just as we did when we referenced the measurement of an angle, mABC.

NYTS (Now You Try Some)
1. Determine the arc measure.
a) / b)
= ______
= ______
= ______
= ______/ / = ______
= ______
= ______
= ______/
Central Angles and Arc Measurement
A central angle of a circle is an angle that has its vertex at the center of the circle and has radii as its sides. We looked at central angles when we discussed the regular polygons. We found that the central angles of the regular polygons were 360/n, where n was the number of sides of the polygon.
Central Angle = 120 / Central Angle = 90 / Central Angle = 72 / Central Angle = 60
The central angle is always equal to the intercepted arc measure. This is a very important relationship for solving many problems dealing with circles.
ABC is a central angle. / Central angle is equal to the intercepted arc measure. / The square has 4  arcs
and 4 central angles. / A diameter is a central angle of 180, thus the arc is also 180.
2. Determine the missing information.
a) Given circle B with as a diameter. / b) Given concentric circles with = 34and
mAJB = 90.
= ______
= ______
= ______
mKBD = ______/ / = ______
mAJH= ______
= ______
= ______/
3. Given a regular hexagon. Determine the missing information.
a) mATB = ______b) mDTB = ______
c) = ______d) = ______
e) mAEB = ______f) If AB = 5 cm, what is TB = ______(E)
g) If AB = 5 cm, what is EA = ______(E) /