Name: ______Date: ______Period: ______Geo w/ Trig Circle Concepts

 The area of a circle is A = r2.  The circumference of a circle is C = d or C = 2r.  If the area of a circle is 25, then the radius is 5, the diameter is 10, and the circumference is 10.  If the diameter of a circle is 20, then the circumference is 20, the radius is 10, the area is 100, and the length of a semicircle is 10.

length of arc measure of arc   circumference 360

area ofsec tor measure of arc   area of circle 360

 In the same circle, all radii are congruent.  A line is tangent to a circle if and only if it is perpendicular to the radius drawn to the point of tangency.  In the same circle or congruent circles, two chords are congruent if and only if they are equidistant from the center.  In the same circle or congruent circles, two chords are congruent if and only if their corresponding arcs are congruent.  If a radius or diameter (or part of a radius or diameter) is perpendicular to a chord, then it bisects the chord and its arc.  If an angle’s vertex is the center of the circle, it is called a(n) central angle. Its measure is equal to the arc.  If an angle’s vertex is a point on a circle, then the angle intercepts 1 arc. Its measure is half the arc, and the arc’s measure is twice the angle’s measure.  If an angle’s vertex is a point inside a circle, then the angle intercepts 2 arc(s). Its measure is half the sum of the arc(s).  If an angle’s vertex is a point outside a circle, then the angle intercepts 2 arc(s). Its measure is half the difference of the arc(s).  If an inscribed angle intercepts a semicircle, then the angle is a right angle.  If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.  If two segments from the same exterior point are tangent to a circle, then they are congruent.  The standard form of the equation of a circle is (x – h)2 + (y – k)2 = r2, where the center is represented by (h, k) and the radius is represented by r.  Two circles are congruent if they have congruent radii/diameters.  All circles are similar to each other.