only provided dec,aeb are straight lines and a and b are tangent to the circles.
Is it possible to prove
(1) adbc is a concyclic quadrilateral
(2) ac=bc?
This question is for compulsory part ,do you think the question provided insufficient information?
photo: http://s613.photobucket.com/user/Yan_Wa_Chung/media/Untitled_zpsxg7iys2x.png.html
plane geometry,plz teach me?
2016-06-17 10:07 am
回答 (2)
2016-06-17 11:29 am
✔ 最佳答案
Question：
Provided DEC, AEB are straight lines and
A and B are tangent to the circles.
Is it possible to prove
(1) ADBC is a concyclic quadrilateral
(2) AC = BC
It is possible to prove (1) and (2) IF
D, E are the intersection points of two circles.
????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
Solution：
Picture：https://s31.postimg.org/e9hg160rf/1234.png
Suppose D, E are the intersection points of two circles.
(1)
∠AED = ∠DAF ...... ( ∠ in alt segment )
∠BED = ∠DBG ...... ( ∠ in alt segment )
∵ ∠AED + ∠BED = 180° ...... ( adj ∠s on st line )
∠DAF = 180° - ∠DBG
∠CBD
= 180° - ∠DBG ...... ( adj ∠s on st line )
= ∠DAF
∴ ADBC is a concyclic quadrilateral. ( ext ∠ = int opp ∠ )
(2)
∵ ADBC is a concyclic quadrilateral
∠BAC
= ∠BDC ...... ( ∠ in the same segment )
= ∠ABC ...... ( ∠ in alt segment )
∴ AC = BC ...... ( sides opp eq ∠ )
????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
20160617
相片：
我們發生某些問題，請再試一次。
2017-04-15 12:01 pm
Question：
Provided DEC, AEB are straight lines and
A and B are tangent to the circles.
Is it possible to prove
(1) ADBC is a concyclic quadrilateral
(2) AC = BC
It is possible to prove (1) and (2) IF
D, E are the intersection points of two circles.
????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
Solution：
Picture：https://s31.postimg.org/e9hg160rf/1234.png
Suppose D, E are the intersection points of two circles.
(1)
∠AED = ∠DAF ...... ( ∠ in alt segment )
∠BED = ∠DBG ...... ( ∠ in alt segment )
∵ ∠AED + ∠BED = 180° ...... ( adj ∠s on st line )
∠DAF = 180° - ∠DBG
∠CBD
= 180° - ∠DBG ...... ( adj ∠s on st line )
= ∠DAF
∴ ADBC is a concyclic quadrilateral. ( ext ∠ = int opp ∠ )
(2)
∵ ADBC is a concyclic quadrilateral
∠BAC
= ∠BDC ...... ( ∠ in the same segment )
= ∠ABC ...... ( ∠ in alt segment )
∴ AC = BC ...... ( sides opp eq ∠ )
????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
20160617
相片：
我們發生某些問題，請再試一次。
Provided DEC, AEB are straight lines and
A and B are tangent to the circles.
Is it possible to prove
(1) ADBC is a concyclic quadrilateral
(2) AC = BC
It is possible to prove (1) and (2) IF
D, E are the intersection points of two circles.
????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
Solution：
Picture：https://s31.postimg.org/e9hg160rf/1234.png
Suppose D, E are the intersection points of two circles.
(1)
∠AED = ∠DAF ...... ( ∠ in alt segment )
∠BED = ∠DBG ...... ( ∠ in alt segment )
∵ ∠AED + ∠BED = 180° ...... ( adj ∠s on st line )
∠DAF = 180° - ∠DBG
∠CBD
= 180° - ∠DBG ...... ( adj ∠s on st line )
= ∠DAF
∴ ADBC is a concyclic quadrilateral. ( ext ∠ = int opp ∠ )
(2)
∵ ADBC is a concyclic quadrilateral
∠BAC
= ∠BDC ...... ( ∠ in the same segment )
= ∠ABC ...... ( ∠ in alt segment )
∴ AC = BC ...... ( sides opp eq ∠ )
????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
20160617
相片：
我們發生某些問題，請再試一次。
收錄日期: 2021-04-20 16:24:25
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