貫二弟張四第
日二十月三年申戊麼優
WAH KIU YAT PO #
B
墓
期墨
曾九月四年八六九一曆公年七十五國民中
168 英文中學會考試題預習專欄
{*** APBQ is
a rectangé:
PQ = AB
數學科
(廿四)
歐陽鋊女
MATHEMATICS (24) LESSON 24 CIRCLES
Example à l'on chords of a cucle) *. Y are the mid-points of the Chords AB, co of a circle centr
0; XN, YM are the perpendicular from X, Y to CD. AB resp If XM
cuts YM at P
prove that op
and xy bisect each other.
PRODE: Join Ox, oy
A
M
x is the mid-point of the chart AB
OX LAB
Since YML AB (given)
PROOF: Since PE, PQ am tangents from P to DA
AP biscots «EPQ Similarly! Ba bisects « PQH
« EPQ = « PQ H
· p = q 2. AP # BQ
[R14.25" GHIEF
att, cs, p=8.
Similarly," AQ, BP are the bisectors of act 43 901, QPF
Similost;
By def.
OX #YM both of In one perp. to CD, OX #PY. anot DY //*!
OY //XN
Qar
APH BQ
*. AQ H ́BP
and APBQ is
AQ #BP #gram.
**A*
48#5%$#$%$# $ # $#%$%$#$#%$%#$%$#$%$##%#$#$%^»$#$%$#%$#$%3 #3%»S
¦ 345%$#543 #ESÉS # BAÆS #53#563 #373 #$%3 #8763
僑
が完
おか
| #$%$#$%$#$%# PELS +5%S#$%$%$#$#%#%#&%$#&%$#&%$#3%83%5/35 +
*#$%$#5%$#$%$ »»5%% #$%$#$%3 #5%$#SFS #3%$#$%$#$%$#$%$#$%$#$%3 #
1968
類習壽酒
歷史科
(廿四)
·嘗一民,
中國歷史科預習問題答案
第七章
第四範
宋朝
北宋的衰焦及未變的南波
ding, of a rect
(十六)選擇題:
1. B
1. C
(十七)填-
題:
1.(A)漭長二年(公元二七)
(B)**
1838 (5)
2.(A)脔天津
(B)
3. (A) Ta
(B)恭
(十八)試分忻北京己上因。
46 BQ on the bisectors of two adj. <s en st. bae GH.
• ARB = ÷ of a des = {a APBD is a rectangle
AB== PQ
PYOX is therefore a ligram Op and XY bisect each othe
Example 2 (Angle Properties of Circle... The bisectors of the angles "ABC, ACB of a ABC intersect at I und cut AC, AB of Y. 2 resp, the circle,
812, CIY meet again of X Prove that «YXZ +<B!C = &Hus FRODE JOM EX, with the notwbians
8,
as shown in hig
in some segment
C,
<7* * - b,
C. CA
b. mb2 (gimn>
<Y*2=EXY + 2732
mt, by
From 18C < BIC + by
Example 3 (Concycké poink )
ABCD is a #gram
O is a pit inside ABC D *.* • AÐB⭑¿COD = 2 É A Prove that.
40BC = <PDC PRODE: Drive APHIDO, BRICO
Since the three sules'of oHBP Qre parnitet do the three sites, of a cao
But
La ABF in ADEO
AB- CR
ARP = &DÇO AS4
C
This live may not Zpass the Zithe ́pt. of inter, of
(< Sum of 4)
Exampk_1: (Alternate Segment:
ABCD is a minor arc of a circh such that AB - BC, AB' and DC meet, when prodead, at P, and DB is produces to meet the tangent AT at T Prove that TP - TA
PROOF
: AB - BC
given és stand on egoat shouts are
AT is a t
1 J. + ABC
▸
A
答:北方四大湖開鎖,初期尚可見作易,但遠至瀾,名號,卒於清康二年微飲二帝慧金|
人巖了你,共联战一百六十八年(九六○二七)。其亡之因,有下列各赠: 1. 外惠想 入球统一之後,國土爲絲燈確的。蔬宋初未能收碟石敬请手 ,形撕防上一大漏洞,泺寫務所乘。此時遼人未服,西邊文考西買 之發物,使中有前後之要,後來源锥气卡金聯兵所亡,但隨之無人很大,代途而成東 北之鬣。卒於北宋亡在金人
2.
大宋之對外政策,只知始展以誤觸,如蜜洲之役,宋兵造凫御金,軍 高清者,本可擊敗兵,奈眞宗思憶,與遼和,而有澶淵之盟訂立。後來西夏及 加入之入要,又未能考於處理,竟約金人降將螢殻,金人乃額此人便,匯成「靖康之
]
#
言时只因 一由於冗兵,冗吏的消解,及對外用兵的支錡, 因而發展•彼况衛書
密支付、夏、魚的錦輝:國際在此躍大的損下,財政駕得不困。
——自于安霾雾相之後,墾中大夫,需了彼此對政局的成見,形成新瀾 黨發、新黨以王安石、承惇、曹布、蔡京無食,而畫業以司馬光、密竊、蘇軾等篇 質。初尙骂了彼此之政見,及安石崩相後,而辦於意氣之爭,一黨得勢,便排斥贏贏
*蕉四十餘年而不息,本與朝政混亂,演耙张。
4.
Lt. sigment
ime segment
sides
Exemple (contact" of "circles)
AB = Þ.
AC = 1
*BAC * fo*"and big 15 the min-pt. of BC. Circits art drawn with 98′′ and AC as diameters? Provm that two circle. can be drawn with O as centa to touch each of these! (Cirottsjand find their cadir, in terms of and ta
(+)***ASONZES) •
答:一、南宇之進寺——他人撰微鉄二一法,乃次螢邦甚爲楚帝,欲以漢制漢,但為臣所贏
· KAREEN • VENDTABAKER=ARX · ****** (EM) › PERSPE ,下開南宋個安之局,此時北方則需金人所撰
二、宋金和刷一遍翩初立之時,任用李箱等相,主要「能守認後能,能觸而後 點
★一時頗想作爲, 奈爾後來高字僧黃潛等、汪伯彥寧願和之擬, 謝烏金人所乘:乃大 無進攻,識金陵,高宗乃奔臨安。此時華韓世忠及其夫人樂紅王於黃天萬大敗金兵,使 魚A因此不敢前含工。不久会人又對象關機,主理河南、陝西之地,以作未会之耀 頓 ,但行有邊整理北方*同時及故意放案牌證,於是備和之又起。其後金人主驗量| *用心發政,讓和中止,乃於紹興小年(公元一叫〇年)再大軍南侯,此時江南軍路 新起來盟瓣義勇軍抗藏,尤以飛之軍勇,於係城(湖北襄關北)大破传兵,並興勝
「趙繫,高達朱仙缱(河南開封西南)正欲攢日渡河,官搗黃龍府,以深二聚、無奈釃和叉 会社
三蔵。 十二金牌谷岡京・後露以「英樹」母飛死帯 「村風羊集和——岳飛死钱,和送成,乃於解關十一年雙方訂約,以大散關為未飲 我長,辛場網臣於念,並常就其金,鍛、蔣合一五萼落聞。未只得回韋太后及微宗之
依據兩宋之形數,求無可觀之將,而建打此品等條約,置乃無療內心隱私。君使南 人心載大受挫折。
中國歷史科預習問題
"Join Of's and produce it to cut DE¦aƒ ̈H K
T OF
When OF AC, & mid↳ point theorem)
£#*EA = ±AB
*OH = ABMACIJE
Similady, OMR OF IFM
AB -- DOC
AQS= – DOC +
Com as
- 408 - ara
Jan Op
O AN | Concyali OC 4 PA OF # BC
Const.
provat
✔
prove
0
Example 1 at chads è Ares)
à ABC inscribes in a circle as shown, D is the roid · pl of minor are BC. O is
A
paint on DA »t. DO=DC Prove that, O is the in DEMİR, of 4 ABC.
PRODE· Join Oc
Minor arc BD =
SUR O
prc.
DC
Given
In the same circle, equal ares subtena igual as las õuj
2,
*
vie DA is the biscotai of BAC
It is required to prove that OC is the bisecto of «¿.
In aon't
\* = 0, + C,
HONGKO
PROOE Let E. F be the mid-pt. of "AB"
"AC mǝp
basra isa o
< DO=DCj
BCA ---GEON, Conclude that
Im ADCO Back
OC is the bisector of From-ai and abo
Example $• ABC is
O is the in-cente of 2ABC
an equilateral a
inscribed in a cireto". P is any poit ca minov are BC, Prové
May
PA = PB+ PC;
PRASE: Prostace BP do 1
suot that
SACPD
PD=PC PC=PD
Const
« CPD = « BAC =60°
chet, a of Cyake junts
2. APCD is equilateral
Consider — APC, BCP -
AC m BC
<ACP = « SCD ( = 60*+ = }
AACPE ABCD
NOTE
wher of thв and FM=FA = £ 40
OM CAB + AC) -.............
From cas and «by, we have « OH = om
with gente o radius on-hik Can Heaw one such circle
msider now,
ON = RF - NA
Hence, with cente
ON and of
radus ok #tip-js
we can draw another rege circle,
As shown in Figure (to the left)). CAMABC is said to be
circumscribed about 00
The Quad
LMNP is said_to_be]
inscribed in
<C> ☺ o is
☺o.
said to be
Circumscribed about LMNP
• ABC
DV
inscribed in
Hues & Aves. To Ex
Then
a*« <p ̃ng+y* = p* * 2p′′g" + gu
[
11, Methet A: Ket amp' + qˆ. b=2pg.
Whea
= +(AB)(AC)
ABC "is tot n
[Merhad B By the area pormula. ftf«a}{3=b}{5 «c)
where
sides of equi a POD
1A/
[Ri Jon AD
AP = &D
swa Bb = B P + PD = BP + PC.
AP = GP+ PC
NOTK w may take a point E on` AP such that_PE=PB
Hence
prove
that aBPC мA ÁBÉ (4&PE
aquilateral), then PC = AE
Example &'( tangents)
As shown in Fig 9,8 ast
is
3,
As parastal lines Gün and EPF, the common tangent
rà fouchés Euch circle
centis of two ciretas touching
as shown. Prove, that
8D = ÷&C
GABA -Źof a #BC × 8 The dist of D fram AB =
Similarly BACD =††
- Ca
the dust. of D from AC = 165km 32 cm
(0) → ABC= APQR = {÷APC + 48¢#
+ LARR) \= 470 - H4x5+20/+3an)
* 17 1⁄2 Cap J 'ham # >8?c. by Pythagoras, A==√P+3* *5 (5.#, i... ant
Roth, 1905-)
第七章
宋朝
第四齡-
第五節
北宋的衰亡及宋室南渡 宋代的學術
thin
Wy:
***AE÷FALA)RAST; (B) REC
C)蒙古嶼】。
1
魚宋帝鷗踏海殉國的忠臣(A)天雅(日)年(
C)秀夫]。
2.
FITURE:
成吉思汗部位以後,即大帶征伐,先發歐三次征,再滿
(A)及(B),然後入主中國。
1. (A)
(B)
宋自(A)關鯛,全都(B),迄微錄二步被據,共有一 百六十八年下,力(C)
2. (A)
(B)
(c)
3.
自高宗迎立於南京起,迄(A)蹈,共 有一百五十二年天下,史(C)
3. (A)
(B)
C)
(廿二)何謂帶廣之難?
(廿三)常宋如何理亡?誠路述之。
(四)宋代理學興盛之因素為何?試說明其效。
世界歷史科預蠲題答案(廿四) ·林希靈 · 芮組 歐洲 (二)經濟及社會的轉變(主要在英國)
(-) RE:
1.
A
(二)檢堑:
1. (A)
2. B
(CROP GATATION) (B)BERR (未完轉入第四張第三貫)
By mid-pl. theorem. "The line joining the two mid-pt. is 14 PRODE
ACD ACB
Vnd 24.03 = 324 324 Nytam XQRD.
•A¢â¤ ̧M + 01+ figrum QPBY AISA DE and AÏ-* AN
#gram XQRD = Agrani QPAY
Exercise 24
SAC - 31 ↑
R
C
1. A triangle ABC is inscribed in a circle, and” the
bisectors of the as meet the 04 « X, Y, Z
{.
12
+++
show
that the as of axY* are resp. 90°-4. 90°- §. 90′′- $
Two circles meet at A and B. AC, AD are diameters, of each circle, Prove that C, B.D are collintar.
3, Two circles meet at A, 6. CD is a commendwegerer"}
to two ciroles. Prove that «CAD+« CBD = 180"
A ABC is inscribed in a circle O is the ortho - centre of a ABC .` Tæp three altitudes AD. BE CF are produced to meet the circle again af G.H. K resp. Prove that O is also the incente of a 6Hk. 5. Two equal chords AB, CD meet, when produciet, at)
G. Prove that BG = DG.
6, ABCD is a cyclic quad. If M, N, P, Q are the
centres of four circles inscribed in 4. ABC, ABD, "ACH, BED. Prove, that MNPQ is a rectangle. 7, The diagonals of cyclic quad ABCD cut each other at st. « at Po Prove that the L from P to BC bisects, when produced, AD. (Brachmæg−)
upta" thewem)
8, AOB, COD a twos 1
Two chard's CP CQ
diameters of a circle cut AB at H, K. Prove that¦
\H, K. Q. P. are concyclic