Applies deductive reasoning to prove circle theorems and to solve problems (p 163)

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10 Οκτ 2013 (πριν από 3 χρόνια και 9 μήνες)

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Heathcote High School


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HEATHCOTE HIGH SCHOOL

YEAR 10

MATHEMATICS PROGRAM

2006

TOPIC
:

Circle Geometry

OUTCOMES
:

Stage 5.3: SGS5.3.4
Applies deductive reasoning to prove circle theorems and to solve problems (p 163)


SUGGESTED TIME
:


CONTENT


KNOWLEDGE AND SKILLS

RESOURCES


TER
MINOLOGY

Key Ideas for Stage
5.3




i摥湴nfyi湧 慮d mi湧⁰慲as ⁡ circl攠
(c敮瑲攬er慤i畳Ⱐ,i慭整erⰠ,ircumf敲敮e攬e
s散瑯爬⁡牣Ⱐ,桯r搬ds散a湴n⁴慮来湴n⁳e杭敮琬t
semicircl攩



畳i湧 瑥牭i湯l潧y 慳s潣i慴敤 睩瑨t慮gl敳⁩渠
circl敳⁳畣栠hs⁳畢t敮搬⁳瑡tdi湧 潮

t桥
sam攠ercⰠ,湧l攠e琠瑨攠e敮tr攬e慮gl攠慴at桥
circumf敲敮e攬e慮杬攠e渠n⁳敧m敮t



i摥湴nfyi湧 瑨t 慲a 睨wch⁡ ⁡湧l攠e琠瑨攠
c敮瑲攠er⁣irc畭f敲敮e攠e瑡t摳



摥m潮s瑲慴a湧⁴桡琠慴aany p潩湴 愠aircleⰠ
瑨tr攠is⁡ u湩煵攠瑡t来湴⁴ ⁴ 攠eircl攬ea湤
瑨t琠th
is⁴慮g敮琠is⁰ rp敮dic畬慲⁴漠oh攠
r慤i畳⁡琠瑨攠e潩n琠tf⁣潮瑡ct



畳i湧 瑨t 慢ove⁲敳畬t⁡ ⁡渠nss畭灴p潮
睨敮 灲pvin朠gh敯r敭s⁩湶潬vin朠ga湧e湴n



灲潶i湧 慮搠dp灬yi湧⁴桥⁦潬lo睩湧 瑨t潲敭s㨠

Chord Properties

Chords of equal length in a circle subtend equ
al
angles at the centre and are equidistant from the
centre.

The perpendicular from the centre of a circle to a
chord bisects the chord.

Conversely, the line from the centre of a circle to
the midpoint of a chord is perpendicular to the
chord.

The perpendi
cular bisector of a chord of a circle
passes through the centre.

Given any three non
-
collinear points, the point of
intersection of the perpendicular bisectors of any
New Century 10 Advanced Ch
15 p432
-

444


New Century 10 Adv & Int BLM
14.4

Excel 10 Advanced
p67
-

76



radius, diameter, circumference,
sector, arc, chord, se
cant,
tangent, segment, semicircle,
subtend, perpendicular, bisects,
equidistant, midpoint, collinear,
supplementary, vertex

1.
Deduce chord, angle, tangent and secant
properties of circles


WORKING
MATHEMATICALLY

DIAGNOSIS/ASSESSMENT



慰ply⁣i
rcl攠e桥潲敭s⁴
灲潶e⁴ a琠瑨攠en杬攠e渠n
semicircl攠es⁡ ri杨琠tn杬攠

(Applying Strategies,
Reasoning)



fi湤⁴ e⁣敮瑲攠潦⁡ circl攠ey
c潮s瑲畣瑩潮

(Applying Strategies)



畳攠eircl攠慮搠潴o敲⁴桥潲oms
瑯t灲pv攠来潭整物c慬⁲敳ults
慮搠i渠灲潢l敭⁳潬vi湧

(
Applying Strategies,
Reasoning)


Heathcote High School


presenterawful_883b0e38
-
98c3
-
4b22
-
b249
-
c382ef5b348a.doc








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two sides of the triangle formed by the three
points is the centre of the circle through
all three
points.

When two circles intersect, the line joining their
centres bisects their common chord at right
angles.

Angle properties

The angle at the centre of a circle is twice the
angle at the circumference standing on the same
arc.

The angle in a s
emicircle is a right angle.

Angles at the circumference, standing on the
same arc, are equal.

The opposite angles of cyclic quadrilaterals are
supplementary.

An exterior angle at a vertex of a cyclic
quadrilateral is equal to the interior opposite
angle.

T
angents and secants

The two tangents drawn to a circle from an
external point are equal in length.

The angle between a tangent and a chord drawn
to the point of contact is equal to the angle in the
alternate segment.

When two circles touch, their centres a
nd the
point of contact are collinear.

The products of the intercepts of two intersecting
chords of a circle are equal.

The products of the intercepts of two intersecting
secants to a circle from an external point are
equal.

The square of a tangent to a ci
rcle from an
external point equals the product of the intercepts
of any secants from the point.