1966-03-22 — Page 14

第二第張四第

1月三年午芮腐豆

WAH KIU YAT F

華僑教育

中中考試題預習專欄欄

英文科

(+3)

英中試題預習專棚

Answers to the previous exercise y

Stammered,

數學科 (十二)

歐陽鋊女•

MATHEMATICS (IZ)"

LESSON GB TRIANGLES JI (The 5 Centers)) ¡ANGLE OF ANY MAGNITUDE,

& THE SOLUnon of EAST

Equations C from 074% 360°)

LSA, The five center of a: Important Theœems

1. The bisectors of the three sides of a ▲ are}

concurrent. C. Circumcentre Theorem.)

The circumcentre is a goudistant from the three vertices 2. The bisectors of the int es of a < are concurrent.

(In-Centre Theorem)

The

in centre is equidistant from the "three sides. 3. The bisector of an int. c and two other ext.i bisectors are concurrent. · (Ex-centre) The medians of a a are concurrent.

Centroid Themem.)

The centroid is of the way along "cach median measured towards the vertex.

5. The altitudes of a o are concurrent.

C Ortho Centre Theorem.)

'car the a

whose vertices are the feet of the altitudes)

is called the pedal triangle of the original <h. If the a is acute-angled, the ortho centre lies inside this.

obluse - angled,

right angled,

Vertex

of the t

**: outside

I on the

*c* Onfocentre is not the centre of any important circle Associate with the a The word "centre" is often used

to denote the

common point of intersection of three,

(or more concurrent st lines

NOTE If the a is equilateral, then the circumcentre.

in centre orthocentre and Centroid are cold 'with each other.

(2) Conversely, if any two of the circum centre

incentre, or the centre and centroid are co- incide, then_the

is equilateral

EXAMPLE 1: Prove that the distance of

orthocentre of a a from a vertex

is tunce the distance of the circon

centre from the opposite side.

Past), Get 0; H be the circumcentre,

· and orkocéntre of ZABC

her M, N be the mid - points.

of HA, HC_resp;

Join MI, PQ.

180_2.80 -QA

1B⋅P-PC'

CPO LEJAC

PD

(Mid-pt. TheokKR),

Similarly, in a HAC MN&ŹAC

Нелс

PQ ABCE LAB1 JOR L'AB

OP LBC ADLBC

ALMN

OQICE

OPVAL

trembled,

plucked

regiment

distress

agitation

indifferent)

obstacle

intense, pledge.

1

spoke besitatingly

shook ..

pulled

"a military"division

pain

emotional disturbance

unooncerned

hindrance,

violent

promise

b. Went through a series of winks and odd faces to as

she winked and make fades to make signs to me severa. 1

times.

was sure she was not indifferent to him

(he was certain she did care for him.

broken off entirely

completely stopped coDIBLY **

better for him to forget"

ication with her.

would do well to forget

дег

o. Major Gordon came to see har.

d. Because she wanted to hide her emotion.

e. Because she wanted the writer to stay behind with her,

f. He made acquaintance with Jessie when he served in the

same regiment with her father, Captain Brown.

6. She was then eighteen.

h. She refused his proposal because she wanted to aurse hei

BLOK 81ster.

1. He knew it when he saw Jessie refused his proposal with..

much agitation and evident

1. Because be thought Jessie was a cold-hearted 1 when

she refused to pledge herself to him as his wife even

when all should be over.

Transisto_the_following into Ezlishs'

日二廿月三年六六九一圈公年五十五國民靠中

沿着荷塘是一條曲折的小煤摩路。這是一个

僚幽僻的终,白天也少人圭,夜晚更加寂寞。 荷塘四面,长着许多樹,蓊蓊鬱鬱的。终的一旁 是些楊柳,和一些不知道名字的樹。没有月光 的晚上,這路上滚森森的有些怕人。今晚卻很 好甜然目光也还是淡淡的。

路上只我一個人,背着手踱着。這一片天地好像

是我的,我也像超出了寻常的自己到了另一世界 裡我爱热鬧,也愛冷静;爱群居,也愛獨處 像今晚上 個人在這荟供的月下什麼都可 以想什麼都可以不想使觉得是個自由的人。 向天裡要做的事一定要說的話现在都可

W

·还是獨的妙惠,我且受用遠旁边的

荷香月色好了。

Hinter

7.4*

荷塘

哼着

眠歌

曲柳

煤消路 出洋

65 £72 12 12.

营牆外馬路上

13 700.

·陰森森

孩子們的歡笑,已经社不到的君主屋滾拍着間 免,迷迷糊糊地哼着眠歌。我悄悄地披了六

热鬧

.這幾天心裡颇不等择,今晚在院子裡生着乘凉 忽然想起甘日走过的价塘

另有一番樣了吧。月亮渐

J

Proof Ket AD, CA be two altitudes

A

M, N be the mid-pt of BC * AB E F be "

GAY GH

QH 2. OM IEF

Q.P. for

3.2

140 224

The car

rastless

lily pond

humming

lullaby

winding

GoalGen-paved pat

remote

exuberan

villon

cleony

Gerry-co-nois

pale

unlimited

cost £187

GHA, by mid point. ThLôEN »,

EF HA

from Example !. we have HA-2 DM

And

EF 2 OM

FEG a.COMG,

EGŹ GA - GM

BFG AMOG

LEGFMGO

ARGO ore collinear

SA.S

comes of way,

cor. sides of' = a,.

OG = GF (= Ź OH) VR. GH = 2 GO

NOTE: OGH is called the Euler Line" of aABC.

Example 4: Solve 3 Cos*B + 3 Sin #=3, for 302020,

Solution

Cost =/- Sato

2 ( 1 ~ Sin*0) + 3 sm 8 – 3

2 Sinė - 3 Sind + 1 = 0

‹ a Sin # -1){ Sin & - 1) = 0

·S in 0-

3,

jinal capital in po 100 mg 4 96 + te df 106m193,

If the car costs A for floo

Then

Hence, A's gain % – 68%

68% of the car

costs -- 2187 762% mt215

As profit -40% of £375 £ 110.

20% of £260 -£52-

The remainder = 1.260 £52 = 108 was divided by Ke

proportion

2000 1200 (1.55)

Ifence. ont veitt share : 2- of £52 + § of x 208 * £ 156,

The other will share. Eabo - KISE -

" If & weighs 10016, then A weigh 100 $120%

"

104

#sih

12:57 of 100- 145 to.. +1916. heavier than A

Cis (125-8÷1516

+1/80+ AND

= 50

50%

5

Rate =

8 guineas

6,

ANS (as

2.4 per cent Crà. 2.4 per 100Ť

16, L-am b

"The sides of a, orqTMHMN are li cach other?

And,

the_int c. are correspondingly equal.

Similarly

H&S MN

***OP&= → HMN

OP≈ HM (= 2 HA),

ie MA-

HC =

ASAJ

Ok - the problem may be proved as follow with centre 0, radius oe, draw the circumcircle) kot BO produced meets the circumcercle at x Then, UY AHCx is a dyran, such that £x="AH

(2) ABCX is # 4 at C and Lop- é cx,

1

If sin b=1 then

43° 150.

Spin 0.1

~ 40°

=30* * 10 # 150 fa stórmó

2

(a) 2:=61

<b>

EXAMPLE 2: If AD, BE, CF are median of AABC,

prove that AD + BE + CF >(AB+ BC+CA). Exemple 5 Solve 3 tan 0 + cot 0 = 5 csc 0.

In a GBC .

G is the controid of a nu

GB4CCej

Similarly, CF + SAD > CA

Adding

EXAMDIE

ZADIRBE AS

> ± (AB + &C + CA)

AD + BE + CF > / (^

If H; GO are resp, the orthocentre, cenhaid And circum Centre of aABC Prove that. TOH,6,0 are callingar, t21 HG =260.

Solution

ம் 8

GOL O

0301

تھ

COLO

-- s (shs)

5 Сра

***

→ S. cos ✪.

Coso + 5 cos 8. 30 (2 cos 0 − 1)( cos 0 + 1) = 0

But co's & Fi

(WHY 33

HINTS & ANS To Ex. 64'

Ket

original ceritel be 100

外

2=22 crepcated i

Exercise CB

If o D E F are reap the intenta, and incent...... of a ABC. Then in the cithocents of

2, ACCE, ACF & are squarts on AB. At outside

BABC Let AHL BC Por that AH, GF • CD,

ar CanoUFFIM

Solve

a,

for values of a between 0° * 360* sinto – è cas off

76°

CH