http://www.ck12.org Chapter 9. Circles
- FindmBĈ(the minor arc). How does the measure of this arc relate tom^6 BCE?
This investigation proves the Chord/Tangent Angle Theorem.
Chord/Tangent Angle Theorem:The measure of an angle formed by a chord and a tangent that intersect on the
circle is half the measure of the intercepted arc.
From the Chord/Tangent Angle Theorem, we now know that there are two types of angles that are half the measure
of the intercepted arc; an inscribed angle and an angle formed by a chord and a tangent. Therefore,any angle with
its vertex on a circle will be half the measure of the intercepted arc.
An angle is consideredinsidea circle when the vertex is somewhere inside the circle, but not on the center. All
angles inside a circle are formed by two intersecting chords.
Investigation: Find the Measure of an Angle
Tools Needed: pencil, paper, compass, ruler, protractor, colored pencils (optional)
- Draw
⊙
Awith chordBCandDE. Label the point of intersectionP.- Draw central angles^6 DABand^6 CAE. Use colored pencils, if desired.
- Using your protractor, findm^6 DPB,m^6 DAB, andm^6 CAE. What ismDB̂andmCÊ?
- FindmDB̂+ 2 mCÊ.
- What do you notice?
Intersecting Chords Angle Theorem:The measure of the angle formed by two chords that intersectinsidea circle
is the average of the measure of the intercepted arcs.
Inthepicturebelow: