Question

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求詳解

演練。
9
10
範例
切線性質的應用(I)
A
如右圖,AABC的三邊分A
如右圖,AABC中, D、
別切圓O於D、E、F三
F
E兩點分別在AB、AC上,
M
點,若AB=6,BC=8,
D
D
E
DE / BC,若圓內切於四
N/
AC=9,圓的半徑為
B
•Ole
C
E
邊形 DECE,M、N、P、Q
B.
5,則:
P
為切點,若AB + BC + CA=
(1) CF-BD =?
A
16,BC=4,則:
(2) AABC的面積為何?
OT
(1) AN= ?
WANTS = SAT
解
(2) DE= ?
解
9
9
9

A
B
A
E.
D
9
9
繼續來挑戰
(1)如圖一,AABC的三邊分別切圓O於D、E、F三點,
若B-7,AC=5,AD=2,則BC=
(2)如圖二,AB、BC、CD分別與圓相切於A、E、D
三點,且AB / CD,若AB=3,CD=2,則圓的半
徑為
9
E
9
9
B
C D
F C
圖(一)

Answer 1

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Mer

AF+FC = AC
(6-x)+(8-x) = 9
x = 5/2
CF-BD = (8-x)-x = 8-2x = 3

ABC面積 = (1/2)*r*s = (1/2)*5*23 = 115/2

Mer

b+c =BC = 4
AB+AC = 16-BC = 12
AN+AQ = 12-(b+c) = 12-4 = 8
AN = AQ = 8/2 = 4

AN+AQ = (AD+DN)+(AE+EQ)
= (AD+DM)+(AE+ME)
= 8是三角形ADE周長

ADE~ABC(AA相似)
周長比 = 邊長比 = 8:16 = 1:2
故DE = BC/2 = 2

Mer

如圖
BC = 8

Mer

藍色線段 = 直徑 = √(5^2-1^2) = 2√6
半徑 = √6

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