Theorems on Circle

• THEOREMS ON INSCRIBED ANGLES

  1. If an angle is inscribed, then the measure of the angle is equal to one-half the measure of its intercepted arc.
  2. If an inscribed angle intercepts a semicircle, then it is a right angle (its measure is 90)
  3. If two inscribed angles of a circle intercept the same/congruent arc, then the angles are congruent.
  4. If a quadrilateral is inscribed in a circle, then the opposite angles are supplmentary.
• THEOREMS ON ANGLES FORMED BY SECANTS AND TANGENTS

  1. If two secants/tangents intersect on the circle itself, then they are forming an inscribed angle whose measure is one-half the measure of the intercepted arc.
  2. If two secants/tangents intersect in the interior of a circle, then the measure of an angle formed is one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
  3. If two secants/tangents intersect in the exterior of a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.
• Congruent Chords: In a circle or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.