Download Example - Petal School District

Advanced Geometry
Circles
Lesson 2
Angles, Arcs, and Chords
In a circle or in congruent circles, two minor arcs are
congruent if their corresponding chords are congruent.
Inscribed & Circumscribed
inside
Quadrilateral
ABCD is
inscribed in
X.
ALL vertices of
the polygon
must lie on the
circle.
surrounding
X is
circumscribed
about
quadrilateral
ABCD.
Example:
A circle is circumscribed about a regular pentagon.
What is the measure of the arc between each pair
of consecutive vertices?
In a circle, if a diameter (or radius) is
perpendicular to a chord, then it bisects the
chord and its arc.
Example:
Circle R has a radius of 16 centimeters. Radius RU
is perpendicular to chord TV, which is 22 cm long.
If m TV= 110, find mUV .
Find RS.
Example:
Circle W has a radius of 10 centimeters. Radius WL
is perpendicular to chord HK , which is 16 cm long.
If m HL = 53, find m MK .
Find JL.
In a circle or in congruent circles, two chords are
congruent if and only if they are equidistant from
the center.
Example:
Chords EF and GH are equidistant from the center.
If the radius of
P is 15 and EF = 24, find PR and RH.
Inscribed Angles & Intercepted Arcs
RST is an inscribed angle
RT is intercepted by RST
1
mRST  mRT
2
If an angle is inscribed in a circle, then the
measure of the angle equals one-half the
measure of its intercepted arc.
Example:
In O, mAD = 140, mBC = 100.
Find m 1, m 2, m  3, m  4, and
m  5.
If two inscribed angles of a circle intercept congruent
arcs or the same arc, then the angles are congruent.
Example:
Find m∠2 if m∠2 = 5x – 6 and m∠1 = 3x + 18.
If the inscribed angle intercepts a
semicircle, then the angle is a right angle.
Example:
Triangles TVU and TSU are inscribed in P with VU  SU .
Find the measure of each numbered angle if m∠2 = x + 9
and m∠4 = 2x + 6.
If a quadrilateral is inscribed in a circle, then its
opposite angles are supplementary.
Example:
Quadrilateral QRST is inscribed in M. If mQ = 87
and m R = 102, find m S and m T.
Probability
size of the event
Probability of an event =
size of the sample space
Example:
Points M and N are on a circle so that m MN = 80.
Suppose point L is randomly located on the same circle
so that it does not coincide with M or N. What is the
probability that m∠MLN = 40?