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Transcript
Circles
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Key things to remember
o Concentric Circles - circles with same center but different radii measures
o Congruent Circles - circles with different centers but same radii measures
o Central Angles - angles within circle with vertex being at the center
o Inscribed Angles - angles within circle with vertex on the circle
o When checking to see if a segment is tangent to a given circle, checking to see if the Pythagorean
Theorem works.
o Tangents to same circle are congruent.
o Tangents cross circle at 1 point whereas secants cross at 2.
o Inscribed polygons are polygons within a circle with all vertices on the circle whereas circumscribed
polygons are polygons that surround a circle with the circle touching all sides of the polygon.
ICA Hints
o pg 443
 #1 Proof can be done in 5 steps. Use the fact that all radii are congruent.
o YTMT: Inscribed Angles #3 since using same arc, set x+21 = 2x -3 to solve for x
Homework Hints
o Pg443
 #2: Done in 4 steps. You will be using either POPBTEE or TPEEEDPB as well as if sides then
angles in this proof.
 #6 & 11: Triangle is one of the Pythagorean triples.
o Pg447
 #12: Dealing with a special right triangle.
o Pg489
 #15: there will be 2 possible answers to this problem. Need to solve a quadratic equation.
o pg 463
 #10: Walk around problem: start off with AQ = x, then AB is split into x and 20-x which in turn splits
BC into 20-x and 11-(20-x). Continue around the problem until you get back to your starting point.
 #12: XZ can be solved using 8 (leg) and 10(hypotenuse).
 #22: ending up with a quadratic equation that needs to be factored.
o Skills 10-5 WS
 #1-2: use Pythagorean theorem
 #3: set PW = QW to solve for x
 #7 & 8: Remember, corners are congruent.
o Skills 10-6 WS
 #2: 180 - 1/2(48+38)
 #4 & #6 - 1/2 of (360-given arc)
 #12: 34 = 1/2(360-x-x)
Quiz Hints
o Anatomy of Circle Quiz:
 Know the difference between concentric and congruent circles
 Know the difference between central and inscribed angles
 Know the difference between secant and tangent.
o Circle Quiz
 Be able to find the measure of a central angle, arc and the length of an arc.
 Be able to solve inscribed angle problems
 Be able to find the circumference of circles.
 Be able to find the lengths of chords.
 Be able to determine the measure of an arc of an inscribed regular polygon.
 Be able to describe the difference between congruent and concentric circles
 Be able to describe the difference between inscribed and circumscribed polygons.
 Be able to write an equation of a circle.
 Review finding the length of chord problems
 Be sure to review past homework assignments.
Exam Hints
o Assessment #6:
 Special Right Triangles – 5 questions
 Angle of Elevation/Depression – 1 question
 Trig Ratios – 3 questions
 Anatomy of Circle – 3 questions (radius, major arc, central angle)
 Circles – 20 questions
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Measure of arc –if dealing with central angle then the same value as the central angle
Length of arc – (measure of arc/360) * circumference of circle
Inscribed quadrilaterals – remember opposite angles are supplementary
When radius is perpendicular to a chord, remember it bisects the chord as well as the arc.
Equidistant Chords- remember they are congruent and they are the same distance from
the center
Distance of a chord from the center is a perpendicular segment
When asked if a segment is a tangent, use Pythagorean theorem to see if it is true.
Walk-around Problem – remember corners are congruent
Be able to find the value of an angle based on where the vertex is. At same time be able
to also find the arc based on the same information.
 Vertex on circle = ½ (arc)
 Vertex in circle = ½ (arc1 + arc2)
 Vertex out of circle = ½(arc1 – arc2)
 Vertex on center = arc
Be able to find the missing segment depending on what kind there is
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Circle Exam:
 10 multiple choice
 5 true/false – be sure to specify why it is false
 5-10 vocabulary – fill in the blank (word bank will not be provided)
 4-8 matching – angle/arc relationship equations
 The rest are solve problems.
 Be sure to review past quizzes/exams