Circle Circle Definition Circle The set of points

Circle

Circle Definition Circle : The set of points coplanar points equidistant from a given point. The given point is called the CENTER of the circle. The distance from the center to the circle is called the RADIUS. Center Radius

Definitions Chord : The segment whose endpoints lie on the circle. Diameter : A chord that contains the center of the circle. Tangent : A is a line or line segment that touches a circle at one point only. Tangent Point of Tangency : ord h C The point where the tangent line intersects the circle. Diameter Secant : A line that intersects a circle at two points. It is a line, ray, Secant or segment that contains a chord of a circle.

Definitions Congruent Circles : Circles that have congruent radii. 2 2 Concentric circles : Circles that lie in the same plane and have the same center.

Polygons Inscribed Polygon: A polygon inside the circle whose vertices lie on the circle. Circumscribed Polygon : A polygon whose sides are tangent to a circle.

ARCS Arcs : The part or portion on the circle from some point B to C is called an arc. B A C If a circle is divided into two unequal parts, the longer arc is called the major arc and the shorter arc is called the minor arc.

An angle with its vertex on a circle that is formed by two other points on the circle is called an inscribed angle For an inscribed angle with the same endpoints as a central angle, the inscribed angle is half the central angle.

If arc Q is 3 cm long in the circle above, and the circumference of the circle is 9 cm, then what is the measurement of the central angle? 3 cm/9 cm = 1/3 The central angle will be the same fraction of 360°. (All circles measure 360°. ). The central angle equals 120°. Therefore, set up a ratio to solve for the central angle measurement. 1/3 = X/360° 1/3 = 120°/360°

In the circle above, arc Q is 30 mm long. The circumference of the circle is 90 mm. What is the measurement of the central angle? 30 mm / 90 mm = 1/3 The central angle will be the same fraction of 360°. (All circles measure 360°. ). The central angle equals 120°. Therefore, set up a ratio to solve for the central angle measurement. 1/3 = X/360° 1/3 = 120°/360°

Given a circle with center B and ABC = 74°, determine the measure of AKC. Central Angle Inscribed Angle For an inscribed angle with the same endpoints as a central angle, the inscribed angle is half the central angle. AKC = 1/2 × ABC = 1/2 × 74° = 37° The Angle AKC = 37°.

Segment AC is the diameter of the circle. If the length of segment BD = 7 inches, inches find the length of segment BE. BE Segment DE is perpendicular to the diameter AC. 7 ? ? Therefore, segment DE is bisected by segment AC. So, the length of segment BE is equal to the length of segment DB. BE = 7 inches