育教僑華頁三第張四第日三十月三年巴展屣夏 WAH KIU YAT PO
郭日僑華
二期星二日九廿月四年九六九一歷公年八十五國民華中
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C文學會考試題預習
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數學科
(廿六)
歐陽女
M
MATHEMATICS (26)
Given: Haram ABCD ROM AD= 6 Case
<A=60° AB= 4-5 cm
175 Cinahuet
LESSON 26
CONSTRUCTION
rect
and utend
area to ABCD
equals 3 cm. Long,
Exampl
Draw a circle of radius 5 cm and inserida. triangle ABC in the circle such that
·CA · A& = 516
Scale
LGASI ES.
BC not such that CF = 3 in.
(2) ·ED and produce if; to mest. BA inducci
at G
(3) Complete the ligram FBGH
(4) Construct rect. DMNE on DE, agual
sh area to DENK.
Then, DENM is the Med. Actonale:
rect. DMNE = ligram KHED. » Ilgram ABCD.
DE - CF = 3 CM
DMNE is the requised re
Construct a circle to pass througn given point ℗ and to touch a given circle,
at a fixed point A
centre
Onstruction : (1) praw i,, an ex-cente of 4ABC.
(2) Drop I,X, LAB prod, I, YLBC, IZLAC (3) Centros A, B, C with radii AX,, BY.
CZ draw 3 circles.
Similarly, for another two ex~cemtes, we have another two possible cases. Together we had
sch of solutions.
HINT & ANS. To Ex 25
bisects <BAC
좋은 음
AB+ AC
-
BD+DC
AC
DC
AB+ AL
AC
Constuction (1) By any scale, draw axy
Zhen
Proof
xample
So that XY = 7 YZ-5; 2X=6
XY!Y* : 2x = 71 5 ÷ 6
12) Draw circle, cembe 0, radius Sco (3) Take a point, say (or B, or A)
on Circumference
(4) Join OC.
(5) Draw the tangent -
(6) Draws BCL=KX,
(7) Join AB
ABC is the required triangle.
e in alt, segment.
A = LBCL = 4x < B=<ACM* <Y
• 3 A B C
XYZ are equiangular « BC: CA+AB = Y2° 2X› XY = S = 6 + 7
Constuct the following fig, (2) anat thɔ Arcs which meet are tangential where they me
unless otherwise indicated.
struction : (1) Jain CA and produce
(2) Join AP.
(33 Draw the pup. bisecta of AP and let
it meet CA produced of o
(34) with centre 0, radius OA, draw
Circle and this is the melt cúcle
Example 5 Construct a circle to pass through two.
given points and to touch a given fine which is net pan Ito the live joining the give. point!
OC BISECTI ABEN AB FAC
BC
Other method
Produce
Produce
·AB+ AC: BC
SA to E s.t. A£=AC
•BO to meet CE at F.
FB bisects EBC BC.
BATAC - EE .ac ..FC.
ADICE
Zin same seg. .vent. opp.. A.A
LADE APB LEPD ・A ABP.
AB BP
DA Sim. • SCDPMS AFP..
SEFPI ACEP
EF BP
(a)
are four AE
6 cm.
egun
fig.(a); AB, BC, CD, DE
quadrants.
FG FK an arcs of radio 6.cm. the distance of # from F # Con
and the line Fit is on aut at
A
Draw, AE
His Draw XA'LAB
and XA =±of 6 a
ta's with centre X, dra
a quadrant A8 IV) Produce XB to Y st. 8y=x8
ama semicircle 50 twi's Produce XY TO Ž
·St. D2=XB
(v) With centre Z
dial guad. DE
(i) Draw axis FH = 6 cm.
in het ram by the radius of v
(6-7)`+ 6′′= (r+63 Apply Pyllagens do diaNG
Lilia Take pl. 0 on FH s.t. Howli (v) Centre 0, draws are GHK (V) Centre F radius 6
Given: St. Ima AB, points P. Q
such that Pa and AB are non-parallal, Construct: Circle(s) to pass diræ P. Q and touch 4B,
:(1) Join PQ and produce it to cut AB of R.
Example
$25 with the. PR. drai
me perpenarcuter of Q;
With Centre R, radus RT donut Semicircle to cut AB at M.N
(4) At M, N, draw EM, FN perp to AB. (5) Draw the perp, bisector of PQ and let..
it meet FM, EN QFE, F MSA.
(6) with centres E, F, radi EM, FN HD,
draws cireles
Then these too die the RESULARE Carcies. Draw any triangle ABC. Without making any measurements, construct three circles, centre A, B, C, 30 that each touches the other kan Give the four possible answers.
·AD, PQ are chords of AQDP
intersect- ig Chods
AC CD.
Similary in BE, PÅ (in PB04)
EC CB = PC CQ Hence Ac CD = EC CB
(AB+BC) : CD = (ED+DC); CB AB+TBC ED+ DC
BC
4) Through A draw DE // BC.
to meet CR prod and
SXPBA APE
AXPC DA APD
BX
AE
= (-)
Hence, R Similary
AZ BX:
BC
AB
BC
red at
CABLY AEAY)
AD andres ABCZ)
BC
想
YA
BC
AD AS
NOTE: DIY This is known as Ceva's thesiem.
(a) The point P can be either inside
outside of AABC There are 7 different possible positions for P (as shown to the right ) (3) This can also be proved
By the fact that in AASP.
theorems
Example
Centre Pad. (6+ (£) Ca draw intersecting ares. cuthing af M. N.
Cenke MN, with pad, 6en dmul arcs.
Draws parallelogram with sides 4.5cm. 6 cm, one of the angle is of 60. Construc a rectangle squal in area to the ligram and with one side 3 cm. long
Construction (1) Draw the inti bisectors of AABC
Let I be the in-centre.
(2) Draws IX LAB, ZYLBC, IZLA (a) with centre A. radius AX, draw a circle. (which will pass thru Z (4) Similarly, for centre 8. radius 81 centre C, radius CZ, draus to circles o
These three are the required Circles
EXERCISE 46
1) construct a line of length 47 cm and measure it Construct a circle to touch a given Ine AB at a given point P. · and a given circle,
centre
Solve, by constuction, the equation Z(9-X)* Draw a square equal in area to a given Notangle.
5. Construct a triangle ABC,
* Which «B=30°
Page 15Page 16
頁四第張四第日王十月三年百巴夏 WAH KIU YAT PO