Download 13-11 review day 1

Name: ____________________________
Review Part 1
Geometry Pd. __________
Date: _____
CENTRAL ANGLES
NSCRIBED ANGLES
VERTEX MUST BE ON THE CENTER OF
THE CIRCLE.
VERTEX MUST BE ON THE CIRCLE.
RULE: ANGLE =HALF THE INTERCEPTED
ARC
13-1
RULE: ANGLE
INTERCEPTED
13-2
Thales Theorem
ANGLES FORMED BY 2 CHORDS
Cyclic Quadrilaterals
“BOW –TIE ANGLES”
VERTEX is NOT on the center and NOT on the
circle.
Quadrilateral inscribed in a
circle
RULE:
13-3
=
ARC
𝑨𝑹𝑪 #𝟏+𝑨𝑹𝑪 #𝟐
𝟐
OPPOSITE ANGLES ARE SUPPLEMETARY (ADD
UP tO 180 )
Watch out! This is not
necessarily a parallelogram,
so consecutive angles are not
supplementary. ONLY
OPPOSITE ANGLES.
SPECIAL INSCRIBED ANGLES
Sneaky Angle
Formed by a Tangent and chord
Rule: ANGLE =HALF THE INTERCEPTED
ARC
SPECIAL CASE
Formed by a secant and chord
Rule: Find the measure of inscribed adjacent angle
and subtract from 180.
If the chord is a
diameter, rt angles!
13-4
ANGLES FORMED BY TWO SECANTS, OR TWO TANGENTS
OR A SECANT AND A
RULE: Outside ∡ =
Special Case- “ Ice cream
TANGENT.
Cone”
Narc + Outside angle = 180
𝑭𝑨𝑹𝑪−𝑵𝑨𝑹𝑪
𝟐
1) Always solve for arcs first. (HIGLIGHT DIAMETERS!).KNOW HOW TO WORK WITH RATIOS!
BIG
CIRCLES 2) Solve the parts in the order they are presented in for the problem.
3) GO SLOW.
4) Highlight parts you're solving for (in different colors).
5) Fill in/mark up the diagram.
Station 1: Arcs and Angles
1) In the accompanying diagram of circle O,
What is the measure of
and
.
?
1) 1040
2) 800
3) 520
4) 400
2) In the accompanying diagram of circle O, chord
̂ = 80.
m𝐴𝐷
What is
?
is parallel to diameter
,
is drawn, and
1) 90
2) 40
3) 130
4) 100
3) In the accompanying diagram of circle O, chords
What is
?
4) In the diagram below,
is tangent to circle O, and
and
intersect at E and
is a chord. If
.
, find the measure of
.
5) Tangents
and
are drawn from point
times the minor arc. Find
.
6) In the accompanying diagram,
to the same circle. The major arc intercepted by the tangents is three
is tangent to circle O at Q and
is a secant. If
and
, find
.
7) In the accompanying diagram of circle O,
,
is a diameter, and radius
is drawn. If
, find
.
8) A quadrilateral is CYCLIC if their __________________________ angles are _______________
Using your answer in #8, answer the following:
8)
.
9)
Station 2: Big Circle Problems
1)
2)
Push yourself!
3) In the diagram, PA is tangent to circle O at A, PBC is a secant, and AB and CA are chords. If m<P = 40 o and
̂ : 𝑚𝐴𝐵
̂ = 7: 3, find…
𝑚𝐴𝐶
̂
a) 𝑚𝐴𝐶
̂
b) 𝑚𝐵𝐶
c) 𝑚 < 𝐴𝐶𝐵
HINT
𝑓𝑎𝑟𝑐−𝑛𝑎𝑟𝑐
Start with
2
d) 𝑚 < 𝐴𝐵𝐶
f) 𝑚 < 𝐶𝐴𝐵
g) 𝑚 < 𝐴𝐵𝑃