MATH theorem

• Arc measure It is the measure of an arc in degrees. it is in the center of a circle. It is dependent on the central angle. • Arc Length It is also the measure of the arc but in actual length. It is also dependent on a central angle. It measures an arc in Units of length such as centimeters, inches, or meters. 75° 75 cm Arc Measure Arc Length ARC ADDITION THEOREM It is a measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

CENTRAL ANGLE THEOREM  it is a measure of the central angle equal to the measure of its intercepted arc.

INSCRIBED ANGLE THEOREM  it is the half measure of the central angle that subtends in the same arc.

SEMICIRCLE THEOREM (180° it is an inscribed angle that intercepts on the diameter of a semicircle. Its measure is always 90°

BISECTED CHORD THEOREM If the diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.

INTERSECTING CHORD THEOREM  If two chords intersect, then the product of the segments of one chord is equal to the product of the other chord.

CHORD ANGLE THEOREM  If two chords intersect in the interior of a circle, then the measure of an angle formed is half the sum of the measure of the arcs intercepted by the angle and its vertical angle

Secant • It is a line on a circle that intersects into two points. • It contains a chord of the circle

Tangent • It is a circle is a straight line that touches the circumference of the circle at only one point.

Secant tangent Theorem . . A B • If a secant and a tangent intersect at the point of tangency, then the measure of an angle formed is one-half the measure of its intercepted arc. m

Two Secant Theorem 1.1; If 2 secants intersect in the interior of a circle, then the measure of an angle formed is ½ the sum of the measures of the arcs intercepted by the angle and its vertical angle.

Two Secant Theorem 1.2 If 2 secants, a secant and a tangent, or 2 tangents intersect in the exterior of a circle, then the measure of the angle formed is ½ the positive difference of the measures of the intercepted arc.

Two Tangent Theorem The measure of an angle formed by two tangents drawn from a point outside the circle is ½ the difference of the intercepted arc.

Tangent – Secant Segment Theorem If a tangent and a secant segment are drawn from the same exterior point, then the square of the length of a tangent segment is equal to the product of the length of the other secant segment and its external segment