1967-04-25 — Page 15

HALL

日六十月三年未丁麼買

WAH KILI YAT PU

fe

#

#1

期

日五廿月四年七六九一屋公年六十五民

試學入大港

行舉起日昨

名餘百四千二生考

名十六百五錄取將

伊烈沙伯與八個進行。 THIO-SHEAF- REELBEK

DE-CUOU - #EBUDE-92

+1.

E-SKYBR. PHI

KL-BEINGLE - NIARSŠ 五百六名,中可放榜。作學佔盡 牛名額 至一百二十名。今年村收中

HOFER - REDZES - EK 香港:李沂意精度下,近年來惓收新

ENDE. (E)

(B5) P

大廚於六十八週年校

14 A 19-232LEK

慶校祝學中英培

觀大洋洋出演富豐序秩日全

̇牌金及狀獎贈獲員職敎深資

分至晚上十一時, 有無視節社,登認項

序 虢 目包括坐行校竪出盘 MT EKO - BR

會中贳比校長致詞,略謂培英之有 、桁濬、唱詩、潑、補、道、 E-EXKAXE.

主持,念吲秩序有銀業燽坐,校歌 校岛祀念佔恩作拜大食,均由谳余新校長

午八時代、中時正及十一時半,分別遷行 ,該校小學斋、初中部、高中部作日 健士出行,該按在社成立三越年校慶 <<-FHVER #*=Terugben. Eya+

-- BRABLER - BXAEKK - <S 全體驚外,挺討韓商名流、賓、校緻 禁禁, 多人,算氣年萍,除該校 捱灣作品,讓他涵露,昨日,該校內 農民狀及紀念金牌,同日在校內舉行學生

片紀念牌揚菜, 在服務安深改进

K<#-#LAHUSLE

及十一時半按對中

• WNKE - 2<538

KY - KRK@ -6

MING-KED

上級際化流行比賽

做人的心栉樣,丼告該析校務

-ETON

;實爲我們

名想見甜妮路• ,彬彬之器,堪蝕爲士林律饴,得獎人姓 BOEREKOSTEKLEBEGE 高鷿念閱勞,恃照門服務紀念金牌」,由 昂校瀲鸷箙煞 啷状」,以安激點;校董會 上才,不乏其人,林委員會頒發「箭民 職員中,嵝忠态怔,運筆服務已譔十年以

楬園餘醋」,並於典禮中,由該校校友 -研由该校元老校友為思英諾醬,題為「 SEƉEZPZEK) -BER+*** 由該校校友忱懂體收師盡,爲「那 KERE

去演,及好校校友排球表演变, 其微F-4-六時校友大會六時五十分的

始前七邪汽球性空等色繽紛,海校區 歇厩望活動,由屮爆三代李榮屯宅蹕,開 下午二胎代起,在紋符大球遇举行的

難道,題為「鸿英與我」,初中紀念會, 小準紀念會,由校元老校友昄说

,凡華燦校四年校友,統上说安员 K

3-DREAMŊEVE#-#

李奕怡小姐佰潔之转校民族舞班演出-

RENELEKOM SEKNKET -

(1)5644-(11)

朵多斑,至深夜十一時綻生插密而散。 CETRNREEKKE - SOEN - A

之口患演,还日昭之口獅凑,柯餘究

-]

#)

貞三第四鱨

-#11

千四百多名

*SAB.

**1-2

11-4

(5

中文中學會考試題預習專欄

£ * * *

IMO & LOG,

BH.HECH.AF

consequently, - AH.HD BH. HECH.HP

NOTE: The converse of the above example is also true.

英文中學會考試題預習專欄

英文科

(廿六)

●英」

數學科 (廿六)

•

歐陽鐇文·

(a)

(b)

[26]))1

AREVETS "Tojtze'previous ́exe roi 901

1. He used to call the boys together and make alreportfor wha‡I

he'bad done in London e

2. Because in the afternoon the boys were suronger in mang ang"

T

he himself was ètemer and harder after some drinks.

No, there was no prospect of any one going away.

4. Phone who had no particular parents to speak of wese unin—

terested at his report.

* The first disappointment was that older'e father bad, not

fully paid his fees. He was two pounds ten short.

5. He quiokened Bolder's reply by the use of the cane.

7. In order to have a good grip of the cane.

B. Because he got warts all over his hande and most important>

that his father had not paid all his fees.

Mr. Squeers as a school master. From the vay ne puna an ea] Bolder ww can say he was a very orusl_man.g

Ia. Boquire

indulge

prevailed

intelligence

reflect

grin

imploringly

Lemanded

thrashing

obtain /

enjoy i

won

pevs

think about!

#tezz

begging A

aaked

whipping

in full assembly —— all gathering together'

had the desired effect ------ produced the wanted result twenty unnecessarily eager voice, ----, twenty voios which'

might not be eager

Exercise 26' Translation

1. Translate the following sa chinese:

It is a curious thing that we busan beings are always} (in search of contrast in our own lives although we aspect

other human beings to be consistent. We often hear some one sight with relief and satisfaction as they describe a friend who is "o ways the same", whereas they complain and protest about another friend because he "blows hot and cold and you never know where you are with him". Let that same person be offered for lunch today just the food he was offered fof lunch yesterday and he will feel that his wife, his mother, whoever should be catering for his boufort is deliberate17 ill-treating him. "Do you expect" he will cry "that a fellow wants to eat the eare old stuff every day of his life?" In some countries, if this lack of imagination in his housekeeper persists it can be deemed "mental cruelty".

Thatever we may think about our own aonaLazy», « anyone who does not love a cool day in summer and c mazu day in winter?: Such a contrast is almost as exciting aar saning upon a gold coin in a box full of old clothes.

VEROL B

As winter gives way to the insinuating whispers of spring. › Woollies become so distasteful we could happily throw away the very coat we were so fond of a couple of weeks earlier, even the devotees of fashion yield to the joy of summer cletten. and last year's silks and cottons come out for the last fling. Bit. cons. high summer itself, and the long light hurid dayg qake us by lethargie ve can soarcely drag ourselves to the beagh, let alone to work. The delights of out-door life sustain us in prospect But pall and dissolve when the longed for time arrives and the clear blue skies that were to Invigorate and enthrall bring weariness and exhaustion. And the shops, if you can drag yourself to the shops, have passed on to thoughts of autumn.

Late.

conela tent

blows hot and bold -

catering ---

daliberately

insinuating -----

devotees

fling

Jathargic

pall

—

7. £

照顧

特意的

抛掉

厳憊

先兆的

速

TR 1 19

invigorate and enthrall

使人安奮

2. Translate Ing Following into English:

TATALATAS 狼彌猴蜡木摅水,則不若鱼鼈;歷險来应,則其

...

使曹深解決了而操跳餘,而震天居嚨敬之小

可不及。令使人而不能,則謂了不育,教人而不能

21293 22 2018 THE B

232

-

"Prince Hang, Sheung

建獨猴

驚

ng instrumentî

and saintgriu)

oaution” a vazing

MATHEMATICS (26)

LESSON 261. SIMILARITY)

IMPORTANT THEOREMS

THEOEK'S ON THE RATIOS OF A ♣ FORKED BY A PARALLEL 3 ×3) If a st. line is drawn parallel to one side of a

then it' divides the other two sides, produced if necessary, proport-) ionally.

2) If a st, "Lane is drawn to GavaSOW SING WADOs of a

same ratio, both internally or both externally, then the st, line is parallel to the third side.

• If AB and CD are transversale of a sou us POLT OLALE VL

500

then, the intercepts made by the parallel lines on AB and ow= CD are in the same ratio,

() As shown in fig. in which 17/06/

shen (1) f=2 (11)44

7111)

{{v}

BC

}

and the converse,

A) THEOREMS ON THE RATIOS FOMED BT ANGLE-DISECTORS:

A

1) The internal - angle bisector of a à divides internally, the

opposite side in the ratio of the other sides of the triangle (And also the converse).....

2) The external – angle bisector or = A GLYLONU ɑzvornally, WON | opposite side in the ratio of the other sidềm of the triangle (the conveten is also true),

21 THEOREMS ON SITIKË TELANCHEST

(1) Bquiangulares (are stille)

2) 3 sides (of are correspondingly ) pro

triangles are similar).

Ratto of 2 sides, inc.,

GOLD

(than,the)

If two aa are of equal altitude (or base), then the ration of their areas is equal to the ratio of their banea(or sal The ratio of perimeters of two similar á ■ is equal tama ratio of two corresponding sides..

6) The ratio of areas of two similar -- -

of the ratio of two corresponding sides.

D) THEOREMS ON THE PROPERTIES OF SIMILARITY OF CIRCLE:

1) Intersecting chords.

2) Tangent property.

130

aquaro

3) If at lines AB, CD are divided (BOTH internally or BOTH'

externally) at X .t. XA.XH XC.ID .Then, the points A,B,C,D are concyclic.

4) If AB is divided externalag av sy VIETNA

a puas not un AB .t.A.XXC2. Then, the circle ABC touches IC at C. EXAMPLE 1: Traposium ABCD with 4D/BC. M,N are

the mid-points of AD BC resp. Prove that BA,CD and MN "when produced are concuzent des

PROOF: Produce BA to meet on

Join ON and 1-2 17 has id at P* In 4 ABN: M2//EN-

OB

In OCN: * M*D//NC (g1ván) From

܂

OBC, AD//BC, we find -

BN = NC (given)

by subst. AMMID

D

If AH.HD-BH.HE, then A,B,D,E are concycile (cont, inter-\

LAES-LADB (in same segment)

secting chords Similarly, BH.HECH.HF BCSF is a cyclic quad./ BECLOTH ( in same segment}

- or, ZBRAZCFA (supp. 8) - Hence, ADBTM ∞ { CPA (= { ABBT) *** A

But, AFDC 18 a cyclic quad. ( for AR.HDCH.HF, given).

Ĺ CFA =¿ ADC (in same aegment}

From (a) & (5): we find (ADB={ADC and BDG is a sv. line»)

AD BO

www VEMIDGentre or 4ABC.)

Carly, DAC & CFAB;' SXAMPLE 5: ABCD is a cyclic quadrilateral.

Prove that: AC.BD=AB.CD+ BC „DAJ PROOF: Draw [ADE=[CDB and let DE meet-

AC at E.

J

[ADE=/BDC

taob

in same *g*}

AAA

[DAE ==/DBC

ADFBDC,

AD: AE BD: BC

1.0.4 AD.BC- BD. AB Since,

ABD4 BCD (^^^)

* AB BD — BC: CD or

AB.D=80.EC

(x) + (b);_ AD,8C +48.CD = RÐ ̧AE÷BÐ ̧EC

= BD(AB+EC) / -BD.AC

NOTE: The converse of UX.5 is also true; and this problam ja

valled Ptolemys' Theorem,

~(b).

EXAMPLE 61 ABC is a triangleja st. lios aute BC produced, CA,

AB at P, Q, R Fosp.; WI in drawn parallel to PQ meste, ing AB at I. Prove that

(a)

1

P

(b) EP1-1

PROOF: (a) Prom o 6PB, CI//PR, -

BP:BCBR:BI

or, BC:BP — BX÷BR

BP-BC: BP HR-BX:BR Á Dividendo

CP:BPXR:ER_

or, B-R

(2) # * #-##-## (sabet.}]

In ACX: RQ//XC

•AGEAL or MM

Hence,

>

WEI KELSA asndo y

(subat.)

A

This problem can also be proved either by drawing CK//AB to cut EQP at K,or by the perpendiculars AL,BM,GN from A, B,C to PQR resp.

The converse of Lisse prvus

** BLEV VEREJNIKA WOKm waenght"|

is known as llenalans' Theorem./

HINTS & ANS" 10 EX. 25.

As in Example 3, 10 m18 car.

10 = pap, Tram # 10 HK=5

Draw on isos. A AHK, bisect AH at de to meet it at 8.

LIBRARIES:

1.0. M' is the mid-point of AD-but i le given as the M.P.)

→ M' coincides with K- 10 ̧M ̧Ñ; are collinearengan Hanes, BA, NE,CD are concurrent, when produced, at 07, NOTE: We have also an alternative proof as follows: Let BA produced meets ? produced at D

"0"

an

OBM AM//BN

In AUREN VDNC

1.4. U and O' are bôto the point divides externally, if at the same ratio.By the unigoness of the point, & ai mast by coincided each other. Hence,BA,CD &N are concurrent, whan 4 produce, at 0.

EXAMPLE 2: P is any pedes ver a puruzwe sajtu sev

two tangenta

from P to the circle. PCD iesa at.line cutting the circle at C & D. Prove that the product of Opposite sides of the quad. AGED are equal,

To prove: AC,BD. BC.AD

PROOF: PA is a tangent of circle ADBC

NZ PKC = ADC

. From

PAC, PDA. ĹPAC = ADP

LAPC APD

/ in alt.06.

proved

Common

NA PAC PDA AAA

19-B

· Similarly, & PBC 2 FDB; ED

PA.PB are tangents from P te sirola ADBC

PAT FB

length of tangent

• 1 A - B or AC BD BC.DA

#

A PEDOF: Produce BC to Dot, CD-AC

EXAMPLE 3: ABC ia an isos, such that /

/B = /02/A. frove that; AB"≈BO*+ ABIBO?

base./0,18ou, A

129=2 ZBAC BAG=/D

(WHATS,

Hence, BA 18 tangent of the sircumcircle of #ACU at A.]

In circle ACD, BA is a tangent and BD is a encant.

· RATM - BC.BD

BCBC+ CD);

tangent property. CAB

for

TAMPLE

FROOF

In ABC1, AD,BE,CF are the altitudes and H is the

orthocentre ofmad ABCsatamaran Prove that: "AH.HD- BH.HE MOH.

His the orthocentre of ABC,

ARBLADE ➡rt.

A, &, D, B are condyolle of

In airols-AEDB ̧«AD & BE...Áre two-chorda, pomylimas quat

WAHIRD - BÃ ‚HE

intersecting chords

SimilarlyTM BCEF 13 a¿ão a cyclis quad. From which,{

with

Solution

221) Divide DC into 3 of parta

(2)

J

<3) Join AQ AP

Tor AC bisects we area of #8C2. And,

APCP==§ of a Acâ

• A¢â«† # A ACD..

20 $ = 1 SEM

Ams EF = int com rangent com. tangent

MN - En

NOTE

1, for MN

BPMN is a

Far EF:

Kgram

BaFE is a gram }

1, we can find toug interior tangémis

• two exterio

common tangents.

hønsverse com tang >5-660x direct com bang, se8-18ca

For calculation. EF * 80 - JAB

hit No BP-

AQ` • JABTM- (AƑ + B£)" AB*- ADA =√Ag` = ( AM-BE)`

* Draw a thea with 4, 5 are the lengils of two adj.

· sides. Apply Pythagoras Relation to the to

5. Sol The two shown ares cof two equator

together. form the locus of vertex A.

* « BIC =180 - And A is fixed

45 mg

A

· LEIC's const.

I will approach to B when # tends to B. .. BIC û part of lo cas AMS The complete locus of I

i's dro.s SIC AUR(BI'CLOS

6. Two methods: Method 1

Method Д

I

** BPN # 90°- 60*» 50-

• «PAN - £ $ 30° = 15? (»«PNA), Mi Draw <BAN = 15' to meet BC at NE)

sti Draw

EN 1 BC to meet AB at Pu

(i) Drow AF IMO TO MELT

Ac produCRL at e

vis Draw the bisector of «AFB

to meet AB at P.

EXERCISE 26

A

1) If is the incentre of ➡ ADÚ, Produce au to cut BC at D. N

Then,

AO:OD #AB+AC1BC.

2) ABCDEP is a hexagon, inac,-~**

AD, BB, CP are concurrent at P, then

paa. Glágonate

3) Two circles most at P, Q. C is a point on PQ, Orawat, izne

_through_C_cuta.the.sirofar-at-iz-D-and-By-E-respu«Prove

AB BOED: DO

4) If,in fig. 4, P. 18 y

inside ABC API, BPT CPZ

are st, lines. Prom that

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