1970-05-28 — Page 22

真二第張六第6日四廿月四年戌庚靨夏 WAH KIU YAT PO

一家服中文中學會考試題預習專欄

淑 學科(三十)

奮仲强•

第廿九次預習題解答

(1) SABC, AD LBC. DEIL,

4B+BD=DC

(設訛如題)

(証明)1.各取 BC, AB的中车

M,N, MN, INMAC

(△两边中奌联线,平行第三边)

2 <1=40(13) A

3

B

ND, 91 BN=DN-AN (stsH1245 98=JI DJ

4.22=18 (等腰三角形角相等)

542-13+41(三角形外角等校内対角和

6 LB==240=23+21=21+2! (nte

21=23 (等量相減)

8 : DN=DM (^4* f#<74) 9. AB+BD÷2AN+BD=RDM+BD (WTA) 10. DC BC BD=2BM-BD=2(BD+DM)−81.

=2DM+BD(全量等於各分量和,代换

G.E.D

11. ^• AB+BD=DC (# * @! <† A (2)任意四边形ABCD中,ADBC之延线交於EXAB, DC ż延线交栓F.<E> <F之平分线方於G求証:

LEGF (<A+<C).

(Eka) EG, FG LAEB,

CAFD=平分线

(TSE) LEGF== (LA+CBCA

SEBA)). AABERAADFY

<A+4ABC +221=180,

<A+LADO+222=180°.

(AmA‡Ž 180, X EG, FG IS A

·41=90-£(<A+ZABC)

H

2 { <2=90 == (<A+ZADC) [14. ¶ 1874)

3.3 FG AD★H, ¦ ¦ AFHD

23-180-LADC-22 (=1+1 140 € 180°)

"24 <3 = 180°-LADC=[90° (<A+LADC)]

=90+= <A-<ADC (***).

5 LE&F=23+21

(△外角等於內对角和

= [90+2 <A-= <ADC]+ 90° - = (<A+ZABC)|

•180° -3- (<ADC+ <ABC). · [fent] 6. THE SOLETY ABCD&, <A+<ABC+<8CD+<ADC=360°.

{ok NAZZJZ)=(<ACC+<ABC)==/ So ~_(<^?«C) † LEGF=180°~ [180°== (<A+2BCD)}=+(<A+LBCD)

(註)本題若槻韻EGLFS則ABCD共 (3) A ABCR =

AD, BE OF CHIC, kal BHXBE+CH CF ĐỊ (設証如題)

(EBA) 1 <1=42=At L

(套线成直角,亿直角等)

2 C, D, HE @ $R

(四边形补角等于内对角,顶要共园)

3. BHBEBDx BC

(國外交弦定理)

4.579\I B,D,H,F*& C^XDF=CDXC8

5 BHXBE+ CH× CF = BDXB C+ CDx CB

— BC(BD+CD) BC2

(12.3)

(+222)

O.E.D

(4) AABC ↑ «AZ§ A 79 17 2 BC = AI SĄ TED, BY

AD + ABX ACBDx CD.

(240) 21=22

(E) AD+ABXAC=BDxCD.

(証明)). 作△ABC的外接园..

(三角形有一且僅有一外挂园)

2. ZE E DA & ABCE, BE,

則 2DCA=<E (园内接四边形外角等於其内的话)

3.42=11-23 (E40, XT

4. ADCACABEA (AS LE TAS DITEMU

AC: AE= AD: AB (相似形之對夜边成比例)

~ ABXACADXAE.

DAXDE=DC1 DB

(國外相交弦定理)

B BDX CD=AD(AD+AE)➡ AD2 + ADXAL DE=PA+AE] 7 AD + ABXAC=BDXCD (**)

QE.D

15)/4 %==} ABC4 # BC ± FR P, E ☎ § 11⁄2 BD-DE=EA

REI ABTAC — AD + AE + 4DE-

(設証如題)

(9) ABE RAADC

·AB+ AE-2 ( AD2+DE3) AD+AC=2(AE+DE3)

(中线走理,亦即阿氏定理:

A

2. AB +AE + AD+AC2=2( AD+DE+AE+DE) [f§*J

3 AB+AC=AD TAE +4DE2 (SIA AD+AEZ)

QED

6) XALA=ATAL BC & 111 14 @ 12 A141014 AT ★ABLA AD=AT, XLR D1FDE LAB Mà ACZ ZE AKE. IXIE AADE-BABC. (已知)BC為0园直径,ATWO园柊T:

·AD=AT DELAB

(TSI) & ADE=AABC,

(THE PA)). TRABOBISF

CF, 128FC=λt.

(半园园周角直角)

2, 1AABC=1⁄2 ABX CF 1AADE=AD× DE

(ᅀ面積等於底典高案積之半八 3. <AFC=st. 2 18 AFB 210)

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四期星日八十月五年〇七九一曆公年九十五鳞民華中 育教僑華

east to the west or recurve to the north- east. Wind speed as well as the amount of

Pan811 Qecrease very rapidly once the

typhoon penetrates inland.

STRUCTURE

OF A TYPHOON

H.K. Certificate or Education Examination (English).

fte ography II

SECTION A Physical Geography

ine following two paragraphs from the South Chin Morning Post describe two natural disasters one of which occurred in a Philippine island south of Manila on the 28th September, 1965 and the other in Hong Kong on the 27th September 1965;

Fát 2.25 8.1,

a giant guen or Ijam snot and rose high in the sky like ared-hot·· cannon ball.... a tremendous explosion shook the ground and rocks and ashes started falling like rain, Fire villages on the island were reported buried under lava and ash....and all vegetation and mostly coconut trees had turned brown from the heat.... Every five minutes or so, thick white smoke would shoot up hundreds of feat."

"A four-year-old boy was killed and three other people injured last night when tons of mud washed down a hill in turrential rain. "A junk capsized off Tsing Yi Island, near Taun Wan, throwing its ten occupants into the choppy sea.

About 20-30 per cent of the New Territorias vegetable crop and from 50-60 per cent of vegetable seedlings were affected by flooding.

dind gusts of 52 knots and 49 knots were recorded at the Observatory and the airport respectively. At the station on Tate's Cairn gusts of 67 knots were recorded.

(a) lame the two natural phenomena described here.

A. A volcanic eruption

Passage of a typhoon

(b) Write a brief explanatory account of the

cccurrence and characteristics of each of them. Description "A suggests that the volcano is of the composite type as both ash and lava are erupted. It is formed by disturbances in the earth's crust which leads to the outpouring of molten material from underneath through a vent. A composite cone will be formed when lava alternates with eruption of agh. The volcanic cone may grow to heights of several thousand feet and have a basal diameter of it. or more miles. Typically the cone steepens toward the summit, giving rise to a symmetrical -shape

A Composite Cone

·ven't.

·lara

Description "B" describe the passage or a typhoon. Typhoon over the North-Western Pacific usually occur at any time between May and November. Typhoons are areas of very low pressure which are formed over wa Bea where there is no friction to hinder air movement. The wind direction in a typhoon over the Northern Hemisphere is anticlockwise and the velocity of such wird

can be very high as suggested in the passage where gusts of 67 knots were recorded,

Accompanying the strong winds, heavy down

urs are not unusual and this may result in flooding of areas near the comst e.g. in

Shatin and Tai Po and landslides are also not infrequent. The general direction of such ty photas la the N.. Pacific is from the

A AFC CO A ADE ( BLAAT, ¿LAR SLATE ANY

AF÷AD=FC:DE (7814#{XZL)

ADX FC DE

(比例式之內項積等於外項精)

AT — AFX AB (+1) #4 /=)

ADX FC.

XAB

DE

the AD

FCX AB

DE

(因知AD=AT等量代換)

8. JADE ==* FCXAB

=2* ABX FC (438)

9. AADE-AABC (KA)

Q.E.D.

(7)OP為定直线见同側两飞如园,求你一直线使嶼

(平行而在該两园内截相等之弦

(已知)O,P為尤直线同侧两已知因,

(求作一直线平行柊见而在OP两.

园内截相等之数,

(19)1130514

DALL, ID PEAK.

PB l

在AD(延長

1 AP-BP.

3. 以P為园心,

7 @ * * * < £ ***

SO

VORTEX

EYE

VORTEX

SECTION B Regional Geography

Section B I

On the sketch map of Monsoon Asia given in Figure 2, draw in the winter and summer pressure system and the resulting winds

(b) Discuss the effect of the monsoon winds on the

climate of Hong Kong..

(a)

Barrier

Sumner Conditions

FIGURE 2.

Mounta

Y

Barrier

LOW

"FOR QUESTION

[Winter Conditions

HIGH

FIGURE 2 FOR QUESTION 5 A

(b) The high and Low Pressure centres formed in the

interior of the Asian land masa cause the North- eastern and the south-eastern monsoons in winter and summer respectively. The winter monsoon period lasts from September to March.. Coastal fogs are common in the Spring months. The summer monsoon, starting from April, brings in the bulk of the annual rainfall. The weather. in summer is continuously hot and humid throughout day and night, cloudy and showery with: occasional thunderstorme. Though Hong Kong da very much affected by the monsoon yet the annual rainfall is erratic, it ranges from 25 inches to 120 inches and unlike the Indian Monsoon where the summer monsoon brings into heavy downpours, the major contributors of rainfall in Hong Kong are thunderstorms, typhoons and temparate depressions. However, the veering of the wind direction is typical of that of a mOND DON climate as the wind is blowing from the north- east in winter and south-east in summer.

To be continued)

17 B 2 OR C.D..

CD并延長之がPBKE,F則此直残が求 ()) BOC=OD, P'C=P'D, by OP'S CD < # ÍF S 1

嗯,又因园二个园,且P’至CD之距離=PEF之距離

by CD=FF

(8)P為见直线外一定要,求在线上取A,B两奌使

• APB A B AB-X & α

(已知)P為直线外一定桌,以马足角,為定長 (*14) Al 1 # + A, B ★ dk LAPB¬× 8 AB=a (作法)1.在线上截任意线段XY==Q 2:以XY為弦,作會之弓形弧,並設其园心為口要。

3 19 014 L * #1 Í m

4. WX P10 OX $ * 13 14 34 I'm 3 T Q, R Q. #£ 5.1XQ; (i=1,2) Â110, 0x £ ¥11 17 @ £ £ £ # 18

& * A; R Bi.

A, B, RA, B. Vý a my

2.E.F