Properties and Relationships of Circles and Their Parts - Prof. Tamela D. Hanebrink, Study notes of Mathematics

Various properties and relationships of circles, including center, radius, chord, diameter, secant, tangent, concentric circles, central angle, minor arc, major arc, semicircle, and their measures. It also covers theorems about inscribed angles, intersecting secants, and tangents. Useful for students of mathematics, particularly geometry.

Typology: Study notes

Pre 2010

Uploaded on 08/08/2009

koofers-user-g7x
koofers-user-g7x 🇺🇸

9 documents

1 / 2

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Circle properties
Circle
Center
Radius
Chord
Diameter
Secant
Tangent
Point of tangency/point of contact
Concentric circles
Central angle
Minor arc
Major arc
Semicircle
The measure of a minor arc
The measure of a major arc
The measure of a semicircle
A line in a plane of a circle and containing an interior point of the circle intersects the
circle in two points.
A tangent to a circle is perpendicular to the radius drawn to the point of tangency.
A line in the plane of a circle and perpendicular to a radius at its outer endpoint is tangent
to the circle.
If in a circle or congruent circles two central angles are congruent, their arcs are
congruent.
If in the same circle of congruent circles two minor arcs are congruent, their central
angles are congruent
In the same circle or in congruent circles, congruent chords have congruent arcs.
I the same circle or in congruent circles, congruent arcs have congruent chords.
A diameter that is perpendicular to a chord bisects the chord and its two arcs.
In the same circle or in congruent circles, chords that are equally distant from the center
are congruent.
In the same circle or in congruent circles, congruent chords are equally distant from the
center.
pf2

Partial preview of the text

Download Properties and Relationships of Circles and Their Parts - Prof. Tamela D. Hanebrink and more Study notes Mathematics in PDF only on Docsity!

Circle properties

Circle Center Radius Chord Diameter Secant Tangent Point of tangency/point of contact Concentric circles Central angle Minor arc Major arc Semicircle The measure of a minor arc The measure of a major arc The measure of a semicircle A line in a plane of a circle and containing an interior point of the circle intersects the circle in two points. A tangent to a circle is perpendicular to the radius drawn to the point of tangency. A line in the plane of a circle and perpendicular to a radius at its outer endpoint is tangent to the circle. If in a circle or congruent circles two central angles are congruent, their arcs are congruent. If in the same circle of congruent circles two minor arcs are congruent, their central angles are congruent In the same circle or in congruent circles, congruent chords have congruent arcs. I the same circle or in congruent circles, congruent arcs have congruent chords. A diameter that is perpendicular to a chord bisects the chord and its two arcs. In the same circle or in congruent circles, chords that are equally distant from the center are congruent. In the same circle or in congruent circles, congruent chords are equally distant from the center.

The measure of an inscribed angle is equal to half the measure of its intercepted arc. An angle inscribed in a semicircle is a right angle. If a quadrilateral is inscribed in a circle, opposite angles are supplementary. If two inscribed angles intercept congruent arcs, the angles are congruent. The measure of an angle formed by a secant ray and a tangent ray drawn from a point on a circle is equal to half the measure of the intercepted arc. The measure of an angle formed by two secants intersecting inside a circle is equal to half the sum of the measures of the arcs intercepted by the angle and by its vertical angle. The measure of an angle formed by two secant rays with a common endpoint outside a circle equals one-half the difference of the measures of the intercepted arcs. Te measure of an angle formed by a tangent ray and a secant ray, or by two tangent rays, with a common endpoint outside a circle is equal to half the difference of the measure of the intercepted arcs. If two chords intersect within a circle, the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other. If two secant segments are drawn to a circle from an outside point, the product of the length of one secant segment and the length of its external secant segment is equal to the product of the length of the other secant segment and the length of the external secant segment. If a tangent segment and a secant segment are drawn to a circle from an outside point, the length of the tangent segment is the geometric mean between the length of the secant segment and the length of the external secant segment.