[Maths] Circles Problems

itphone

白手用電腦畫係差d.....
兩幅圖O點均是圓形圓心

圖1:

第 a) 題証明全等我識
但 b) 題証明孤長一樣就唔識

請大家教教小弟

圖2:

點証AD同DC孤長一樣?

dolphin_ice

1b 3角形中間係個diameter, 即係ABD係 isoceles (差唔多啦) triangle. 即係BE=DE, 所以BC=CD

2 AB=BC, across diameter and center, therefore, A and C have the same distance from B and O. AB=CB, AO=CO
Hence, AD=DC

細薯

Originally posted by 紅唇娃 at 2005-3-5 11:51 PM:
1b 3角形中間係個diameter, 即係ABD係 isoceles (差唔多啦) triangle. 即係BE=DE, 所以BC=CD

2 AB=BC, across diameter and center, therefore, A and C have the same distance from B and O. AB=CB, AO=CO
...

1b

BE=DE, 所以BC=CD

i don't understand...

question 2 also.......
================================
my answer:
1b

if triangle ABE and triangle ADE are 全等(forget jor the English term),
angle BAE = angle DAE
therefore, arc BC = arc CD (arc prop. to angles at circumference)

Question 2 similar to 1 b
prove the two triangle are 全等(SSS)
then
use property
PS:
but the property is not
(arc prop. to angles at circumference)
it is
(arcs prop. to angles at centre)

[ Last edited by smallpotato226 on 2005-3-6 at 04:57 PM ]

dolphin_ice

BE同DE ge距離一樣﹐因為係等腰3角型

細薯

Originally posted by 紅唇娃 at 2005-3-6 07:55 PM:
BE同DE ge距離一樣﹐因為係等腰3角型

但這樣可以證明BC=CD 的嗎?

carrie01li

Originally posted by smallpotato226 at 2005-3-7 01:56 PM:

但這樣可以證明BC=CD 的嗎?

可以, 因為佢証明arc BC=CD by (eq. angles, eq. arcs)

抹茶可樂

1
a) SAS
b)
∠BAE=∠DAE
Hence BC=CD

2
△AOB=△COB (SSS)
∠ABO=∠CBO
Hence AD=DC

細薯

haha
都係唔明XD
=====================
to落雷:
"如果"CE可以ng寫/背property 落去嗎?

dolphin_ice

BE同DE ge距離相同﹐咁係咪即係BC 同DC=
因為C係E直落咋喎﹐而E係diameter

抹茶可樂

Originally posted by smallpotato226 at 2005-3-8 10:38 AM:
haha
都係唔明XD
=====================
to落雷:
"如果"CE可以ng寫/背property 落去嗎?

堆reason自己填返

CE有時會叫你唔駛寫reason
(原因是佢想陰人，唔駛寫reason的時侯就會有人用直覺)