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 = 2r. 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. .