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D1

 ELEMENTS OF A CIRCLE


Circles are characterized by having all their points with the same distance from a fixed point. The fixed point is called the center and the distance from the center to the circumference is called the radius. The most important parts of the circle are the center, the radius, the diameter, the chord, the tangent, the secant, and others.


Center

The center is defined as the fixed point that is located inside the circumference. This point is equidistant from any point on the circumference.


Radius

The radius of a circle is the constant distance from the center to any point on the circle. The radius is generally represented by the letter r.


Arc

The arc is defined as a portion of the circumference. The arc is bounded by two points on the circumference. An angle is used to measure the arc.


Chord

The chord is a line segment that is located on the inside of the circumference and that joins a pair of points on the circumference.


Diameter

A diameter is a line segment that joins two points on the circumference and passes through the center. Diameter is also defined as a chord that passes through the center. The length of the diameter is exactly twice the length of the radius.


Tangent

The tangent is a straight line that passes through the outside of the circumference and touches it at a single point.


Secant

The secant is a straight line that passes through the inner part of the circumference and is touched by two different points.


Inscribed angle

At an inscribed angle on the circumference, the vertex is located at a point on the circumference. Also, the sides are formed by two chords of the circumference.


Central angle

At a central angle of the circumference, two radius form its sides.


PRACTICE

Identify tangents, secants, inscribed angles, central angles, arcs, chords, radius, chords and center in the following Circle. 









Theorem 1: The measure of an inscribed angle is half the measure of his intercepted arc or central angle

Theorem 2: The measure of an angle formed by a tangent and a secant, or by two secants, from an exterior point to a circle is equal to half the difference in the measurements of the intercepted arcs.




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