1970-05-31 — Page 14

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英中會考數學(三)答案

育教、僑華

英中會考數學(二)答案

( 籟 ) - 堅道英文書院撰答

14.(a

Givens AB in the tankent of

O AFC

Užvent AD

ED

BE EQ

AELEB

CFED is a at." line

to prove: AFBD is a //gram. Proof:

Lax, = LI (ext / cyclic

A AFE, BDE

ruad,

L (Ls in alt-

segment)

L52

Lx, (La în the

To prove : DEFG is a cyclic quad

Proofi

Since D, 0, 5 are mid-pts, of 13, BC, AC

same sapment.)

rasps otively

DG

BC

DE

AC

GF

AB

LI - LI1 (OPD. Ls of // gram/

堅道英文書院撰答

Suggested Answer

of

.K. Certificate of Education Examination (English)

Section A

Mathematics III

(1) The polygon has 12 sides.

(2) Area of AABE - 9 sq.m.

3) area of inscribed oirola

area of circumscribed circle

(4(a) rectangle, squar

(b) square

(c) Thọabus

(5) DC the longes

"AB is the shortest

6) The locus of P is a straight line passing through

F parallel to BC

(7) only (d) is wrong

AB - BE (given)

ADF BED (vart. opp. / s

• 13 (proved)

AAFE ABDE {A.A.Ş.

* EM

DE

AFBD is e

orr. aidea of conguent As)

gran (diag. bisect each other)

_x. (corr./ 8 UG // EG

L3

LX (alt. Lo DG // EC)

AGN, FON

NP (intercept Th.).

Given

B

ABCD 18 a

//gran

LONY

GNA - 90° (alt. / e DG // BC)

E in any pt. sing AABD

(9

CN common

To provas ABEC -

ABED

rroof: AAEB

ADEC-

ABCD

ABEC

ABOD (ДАЕВ

ADEC)

AAED

HABOD - AET

17.(a)

AABB + ABED - SABCO - AED

ABEC-AAEBAREL

GAFIN (S.A.S.).

(corr. /s of congruent (s).

dince / EFG + × • 180° (adj. is on a st.

EFG

180*

line)

DEFG is a cyclic quadrilater

I want ABCDE is a regular

pantagon

To prove: AB+ B- A

Proof

Each int. of the pentagon

1080

800

72

FG

Given ABFE, BCGF, CDHG are 3 oonė

of each side 'equals to

To próvas (1)

36

AF

FH

(25)

Proofi

L

OF PR

(sidea opf, oqual (8)

AB+ B AE + BP.

2a (Pyth. Th.)

s(2a)

EP + BP

BE

• AG

(11) tanla

FG FH

cantarir

- tangtann

(C)

17.(b) Let a, b be lengths of two lines, in which

La longer than b..

date methou::wing or cusana rorm

@pplicablm).

Givens In

ABC

A

90°

To prove

Froofi

AN AN

- AB+ AC BC).

BM: BP

ON

CP

Since AMON 18 a rectangle

AN AC CH 40 -AN-AB- BK - AB

• AB + AC ~ (OP + BM)

(AB+ AC - BG)

ja + b) 2

* b)

Lab)

(a - b)

+4ab

23

(20)

(10)

(11)

Diameter

Set square:

ADE, ABC are similaz

鍋子

BD

is the given pt.

APB is the longest chord

which must pass through the

centre, and CPD in the shortest chord which mua † perpendicular to AB.

OP

132-

12 O

a

from measurement, lengths of the two lines are

232 co

and a 10.9 ca

Constructions -

1 Draw BQ- BO + CA

2. Take any pt. Non BQ erect a perpendicular

MN-equals stoTABASA

3. From M.construct a line MP //-3Q

At B construct an angle equals to the given

and meet MP at A

Draw the perpendicular bisector of AQ and let

it out BQ at C

ABC is the required

Section B

(12)

EN

ER 2

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