Parts of a circle

Learning Objectives Identify and define the key parts of a circle: radius, diameter, chord, secant, and tangent. Differentiate between a major arc, a minor arc, and a semicircle based on their measures. Define and identify central angles and inscribed angles and their corresponding intercepted arcs. Apply the relationship between a central angle and its intercepted arc to find unknown measures. Apply the Inscribed Angle Theorem to find unknown angle or arc measures. Use the Tangent-Radius Theorem to solve problems, often in conjunction with the Pythagorean theorem. Ever wondered how a pizza is perfectly cut or how satellites maintain their orbit around the Earth? 🍕 It all comes down to understanding the fundamental parts of a circle! This tutorial will dissect the circle,...

TermDefinitionExample Radius (r)A line segment from the center of a circle to any point on the circle. All radii of a given circle are congruent.In a circle with center O, if A is a point on the circle, then the segment OA is a radius. ChordA line segment whose endpoints both lie on the circle. The diameter is the longest possible chord of a circle.If points B and C are on a circle, the line segment BC is a chord. Diameter (d)A chord that passes through the center of the circle. Its length is twice the length of the radius.If chord BC passes through the center O, then BC is a diameter. SecantA line that intersects a circle at exactly two points. It contains a chord.A line that passes through points D and E on a circle is a secant line. TangentA line in the plane of a circle that intersect...

Diameter-Radius Relationship d = 2r The diameter (d) of a circle is always twice the length of its radius (r). Use this to convert between the two fundamental measures of a circle's size. Central Angle-Arc Measure Theorem m∠AOB = m(arc AB) The measure of a central angle (in degrees) is equal to the measure of its intercepted arc. This provides a direct link between an angle at the center and a portion of the circumference. Inscribed Angle Theorem m∠ABC = \frac{1}{2} m(arc AC) The measure of an inscribed angle is exactly half the measure of its intercepted arc. This is a crucial theorem for finding angles when the vertex is on the circle, not at the center. Tangent-Radius Theorem A tangent line is perpendicular (⊥) to the radius at the point of tangency....