Chords and Arcs+ Other Geometry Conjectures for quiz

Remember

(a+b)^2= a^2+2ab+b^2

Equation of a Circle

(x - h)^2 + (y - k)^2 = r^2, with the center being at the point (h, k) and the radius being "r".

Circumference

2πr or πd

Arcs by Parallel lines

A line that intersects a circle in two points is called a secant. A secant contains a chord of the circle and passes the ought interior of circle AB is a secant

Cyclic Quadrilateral

A quadrilateral inscribed in a circle Each of its angles is inscribed in a circle Each of its sides are chords of a circle

Tangent

A tangent to a circle is a line in the plane of the circle that intersects the circle at exactly one point

Angles inscribed in a semicircle conjecture

Angles inscribed in a semicircle are right angles

Common Tangents

Common tangents are lines or segments that are tangent to more than one circle at the same time.

Theorem 12-15

For a given point and circle, the product of the lengths of the two segments from the two segments from the point to the circle is constant along any line through the point and the circle

The measure of an angle formed by a tangent line and a chord is

Half the measure of the intercepted arc.

Inscribed Angle

Has its vertex on the circle and its sides are chords The arc formed by an inscribed angle is twice the measure of the inscribed angle.

Chord Arcs Conjecture

If two chords in a circle are congruent, then their intercepted arcs are congruent

Chord Central Angles Conjecture

If two chords in a circle are congruent, then they determine two central angles that are congruent

Theorem 12-9

In a circle if a diameter bisects a chord that is not a diameter, then it is perpendicular to the chord

Theorem 12-10

In a circle the perpendicular bisector of a chord contains the center of a circle

Theorem 12-8

In a circle, if a diameter is perpendicular to a chord, then it bisects the chord and its arc

Inscribed Angles Intercepting Arcs

Inscribed angles that intercept the same arc are congruent

Parallel lines intercepted Arcs conjecture

Parallel lines intercept congruent arcs on a circle

Hat Theorem

Tangent segments to a circle from the same external point are congruent.

Central Angle

The central angle is equal to the measure of the arc that measure forms A central angle has its vertex at the center of a circle

Theorem 12-13

The measure of an angle formed by two lines that intersect inside a circle if half the sum of the measure of the intercepted arcs. m<1= 1/2 (x+y)

Theorem 12-14

The measure of an angle formed by two lines that intersect outside a circle is half the difference of the measures of the intercepted arcs m<1= 1/2 (x-y)

Inscribed Angle Conjecture

The measure of an angle inscribed in a circle is one half the measure of the central angle

Cyclic Quadrilaterals Conjecture

The opposite angles of a cyclic quadrilateral are supplementary

Perpendicular Bisector of a chord conjecture

The perpendicular bisector of a chord passes through the center of a circle

Perpendicular to a chord conjecture

The perpendicular from the center of a circle to a chord is the bisector of the chord

Chord Distance to center conjecture

Two congruent chords in a circle are equidistant from the center of the circle

If a line is tangent to a circle,

it is perpendicular to the radius drawn to the point of tangency

Circle Area

πr^2