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请问这道题怎么解答?谢谢
1个回答
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(1)
OD=OB
OC =OC
∠OBC=∠ODC =90°
=>△ODC≌△OBC
=> BC=CD
(2)
∠EDB=90°
∠ADE=∠EDB-∠EDO
=90° - ∠EDO (1)
consider △EDB
∠EDB+∠DEB+∠EBD=180°
90°+∠DEB+∠EBD=180°
∠EBD=90°-∠DEB
∠ABD=90°-∠DEO (2)
(1)=(2)
∠ADE =∠ABD
(3)
consider △ADO
|AD|^2 =|AO|^2+|OD|^2
4=(1+r)^2 +r^2
2r^2+2r -3 =0
r=(-1+√7)/2
直径=2r =√7-1
OD=OB
OC =OC
∠OBC=∠ODC =90°
=>△ODC≌△OBC
=> BC=CD
(2)
∠EDB=90°
∠ADE=∠EDB-∠EDO
=90° - ∠EDO (1)
consider △EDB
∠EDB+∠DEB+∠EBD=180°
90°+∠DEB+∠EBD=180°
∠EBD=90°-∠DEB
∠ABD=90°-∠DEO (2)
(1)=(2)
∠ADE =∠ABD
(3)
consider △ADO
|AD|^2 =|AO|^2+|OD|^2
4=(1+r)^2 +r^2
2r^2+2r -3 =0
r=(-1+√7)/2
直径=2r =√7-1
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