Math Test 10.2-10.8 4/27/18
How many radians is a full circle?
2 Pi radians
What is a sector?
A chunk of area in the circle.
What does circumscribed mean?
A circle is circumscribed about a polygon if the circle contains all the vertices of the polygon.
What is a circumsized polygon?
A circumcised polygon has vertices that do not lie on the circle, but each side is tangent to the circle.
What is a tangent?
A line is a tangent to a circle if it intersects the circle in exactly one point.
What does inscribed mean?
A polygon is inscribed in a circle if each of its vertices lie on the circle.
What is a secant?
A secant is a line that intersects a circle in exactly two points.
What is a segment?
A segment of a circle is a region bounded by and arc and chord
Formula for a triangle area?
A= 1/2(B*H) You may have to use trig. and cut the triangle in half to get height. Sin=O/H Cos=A/H Tan= O/A. If not that, then you will need to use special right triangles.
What is an incribed angle?
An incribed angle is a angle that has its vortex on the circle.
In a circle, what direction do you rotate?
Counter-clockwise
What must the measure of a major arc be?
Greater than 180 degrees.
Tangent to a circle Theorem
If a line is a tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.
Converse of Tangent to a circle Theorem
If a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle.
Inscribed Quadrilateral theorem
If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.
Secant and Tangent theorem
If a secant and a tangent intersect at the point of tangency, then the measure of each angle formed is one-half the measure of its intercepted arc.
Secant and a tangent segments theorm
If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.
Inscribed angle theorem
If an angle is inscribed in a circle, then the measure of the angle equals one-half the measure of its intercepted arc ( or the measure of the intercepted arc is twice the measure of the inscribed angle.
Inscribed Angle in a Semicircle theorem
If an inscribed angle intersects a semicircle, the angle is a right angle.
Cross Segments Theorem
If two chords intersect in a circle, then the products of the measurements of the segments of the chords are equal.
Congruent Inscribed Angles Theorem
If two inscribed angles of a circle ( or congruent circles) intercept congruent arcs or the same arc, then the angles are congruent.
Two Secants Segment Theorem
If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant and its external secant segment.
Theorem for Secants
If two secants intersect in the interior of a circle, then the measure of an angle formed is one-half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
Another Secant Theorem
If two secants, a secant, and a tangent, or two tangents intersect in the exterior of a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.
Two tangents to a circle theorem
If two segments from the same exterior point are tangent to a circle, then they are congruent.
Arcs and Chords
In a circle or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.
Theorem: Diameters and Chords
In a circle, if a diameter or radius is perpendicular to a chord, then it bisects the chord and its arc.
Theorem: Congruent Chords
In a circle, two chords are congruent if and only if they are equidistant from the center.
Theorem
In the same or congruent circles, two arcs are congruent if and only if their corresponding central angles are congruent.
What are adjacent arcs?
Like adjacent angles, adjacent arcs share one endpoint.
What are the two types of arcs?
Major arcs and minor arcs
How to find the area of a segment?
Minus the area of the triangle it is apart of from the sector it is apart of.
What are the two forms of writing the equation of a circle?
Standard and General
What is the measure of a Minor arc equal to?
The central angle and <180 arcs
How to calculate Arc Length?
The circle represents the degree of the arc
How to find a sector?
x stands for the central angle of the sector you are trying to find.
