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Angles of intersecting chords theorem.Formula for angles and intercepted arcs of intersecting chords.This page: Angle formed by intersecting chords | Tangent and Chord|| Related Pages: Circles forumula, graph, equations | Equation of A Circle | Circumference | Area | Chord |Arc | Inscribed Angles|Secant of circle | 2 Tangents from 1 point | Tangents, Secants, Circles Theorems Angles formed by intersecting Chords
Theorem: The measure of the angle formed by two chords that intersect inside the circle is ½ the sum of the chords' intercepted arcs.
 In the diagram on the left, the measure of x is half the sum of the intercepted arcs (arc TE and arc GR)
Use the thoerem for intersecting chordsto find the value of sum of intercepted arcs (assume all arcs to be minor arcs).
Answer By our theorem, we know that x = ½(arc TG + arc ER) x =½(75 + 65) x =½(140) x = 70°
Use the thoerem for intersecting chordsto find the value of sum of intercepted arcs (assume all arcs to be minor arcs).
sum of arcs By our theorem, we know that 110° = ½(arc TE + arc GR) 2 •( 110° = ½( TE + GR)) 220° = (arc TE + arc GR) Therefore the sum of them easures of minor arcs TE and GR is 220 °. Find the is the measure of
 AEB and CEDMeasure of Angles 
AEB = ½(arc AB + arc CD)
AEB = ½(30° + 25°)
AEB = ½(55°)
AEB = 27.5°m AEB = mCED since they are vertical angles.
What is wrong with this problem, based on the picture below and the measurements on the left? Answer 
The problem with these measurments is that if angle AEC = 70°, then we know that arc ABC + arc DF should equal 140°. Therefore, the sum of the two remaining arcs, arc ABC and arc AGF should equal 360°- 140°= 220°. So far everything is fine. However, the measurements of arcs AGF and CD do not add up to 220 ° 170 + 40 ≠220Therefore, the measurments provided in this problem violate the theoream that angles formed by intersecting arcs equals teh sum of the intercepted arcs. Top |
