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A closed plane curved all points which are equidistant from a point within called the CENTER.
Length of a cirlce.
A line segment joining any two points on the circle.
Secant and Secant Segment
Secant lines touches exactly 2 different points
Secant segment is a part of secant line but has its endpoint outside the circle
Tangent lines are lines that touches exactly one point called point of tangency
Tangent segment is a part of a tangent line between the point of tangency and an point outside the circle
is a line that is tangent to each of two coplanar circles. Example: CD and FD
Common Internal Tangent
is a common tangent that intersects the segment joining the centers of two circles. Example: FD
Common External Tangent
is a common tangent that does not intersect the segment joining the centers of two circles. Example: CD
Segment ( Segment of centers)
– is the segment whose endpoints are the center of two circles
- is an angle formed by two radii, so its vertex is the center of the circle and the radii are the sides.
- is an angle whose vertex is a point on the circle and whose sides are chords. A central angle is a inscribed angle but its vertex is on the middle that is why it has a different name. A inscribed angle should have it’s vertex inside the circle otherwise it may not be called an Inscribed Angle.
- any portion of the circumference of the circle.
Classifications of Arc:
- an arc equal to half of a cirlce (180˚)
- an arc less than semicircle (1˚-179˚)
- an arc greater than semicircle (181˚-359˚)
*arcs can be measured in usual
linear units or in arc degrees
- measure of an arc intercepted on a circle by the sides of a central angle of 1˚
- an arc formed when segments intersect portions of a circle.
Sector of a circle
- the figure bounded by 2 radii and the intercepted arc; region enclosed by the central angle of a circle and the circle itself.
Segment of a circle
- figure bounded by an arc and its chord
- a polygon circumscribed about a circle, with each side of which tangent to a circle. The circle is said to be inscribed in the polygon. The center of this circle is called incenter of a polygon
- a polygon inscribed in a circle, with each side of which is a chord of the circle. The circle is said to be circumscribed about the polygon. The center of the circle is called the circumcenter of the polygon
center of a regular polygon
is also the center of the circumscribed and inscribed circle
radius of a regular polygon
is the radius of the circumscribed circle
apothem of a regular polygon
is the radius of the inscribed circle
central angle of a regular polygon
is an angle formed at the center by any two adjacent vertices of the polygon
congruent or equal circles
are two circles whose radii are equal or congruent
are two or more circles with a common center but their not equal
are circles that intersect at two distinct points
are two circles that are tangent on the same line at the same point
circles are two circles whose centers are on the same side of a tangent line
circles are two circles whose centers are on the opposite sides of a tangent line
Projection of a point upon a line is the foot of the perpendicular from the point to the line.
The projection of a point on a line when it is external to the line i.e. a point not belonging to the line is "A point that represents the foot of the perpendicular drawn from the point to the line".
Projection of a line segment upon a line is the locus of the projections of all the points of the segment upon the line.
Locus of a point is the path which contains all the points and only those which satisfy certain given geometric conditions.
The locus of points at a given distance from a given point is a circle whose center is the given point and whose radius is the given distance.
of two quantities is the quotient obtained by dividing one number by another
Three ways to write Ratios:
Word notation = A is to B
Odds notation = A : B
Fractional notation = A/B
is the equality of two ratios. Each of the four quantities of a proportion is a term. The first and the fourth are the extremes; the second and the third are the means
is a proportion in which the second and third terms are equal.
A line segment from the center to any point on the circle.
A chord passing through the center of the circle. It is also the longest chord that can be drawn on a circle.
Solid Geometry by Clarita R. Guevara, http://quizlet.com/10057417/print, http://www.sparknotes.com/math/geometry1/circles/section2.rhtml
, http://www.mathwarehouse.com/geometry/circle/arc-of-circle.php, http://www.sparknotes.com/math/geometry1/circles/section2.rhtm