elahism的部落格

標題:

F5 Maths

發問:

• 點整CS人數1 VS 4
• 想自學英文有咩辦法-- _ -請救救小弟@1@
• Canon 50mm f1.8 II 可以用在Canon SLR 30v 嗎-@1@

 

此文章來自奇摩知識+如有不便請留言告知

Figure: http://img291.imageshack.us/img291/1535/50487666.jpgIn Figure , two circles intersect each other at two points A and B. PQ is a common tangent to the two circles and touches them at points C and D. DB produced cuts AC at F and CB produced cuts AD at E.a) Prove that angle CBD + angle CAD =... 顯示更多 Figure: http://img291.imageshack.us/img291/1535/50487666.jpg In Figure , two circles intersect each other at two points A and B. PQ is a common tangent to the two circles and touches them at points C and D. DB produced cuts AC at F and CB produced cuts AD at E. a) Prove that angle CBD + angle CAD = 180 b) Prove that A, E, B and F are concyclic. c) Prove that triangle DAF ~ triangle DBE. d) If BD = 2, ED = 1 and AE = 4, find BF

最佳解答:

圖片參考：http://imgcld.yimg.com/8/n/AC06565267/o/701010130063713873377220.jpg Qa. ∠BCD= (arc BC)/2 = ∠CAB ∠BDC= (arc BD)/2 = ∠DAB so, ∠CBD+∠CAD=∠CBD+∠CAB+∠DAB=∠CBD+∠BCD+∠BDC=180 Qb. ∠FBE+∠FAE=∠CBD+∠CAD=180 so, A,E,B,F are concyclic. Qc. ∠ADF=∠BDE ∠DAF=180-∠FBE=∠DBE so, △DAF~△DBE (AA) Qd. DA:BD=DF:DE (since △DAF~△DBE) 1+4 : 2 = 2+BF : 1 5=2(2+BF), so, BF= 1/2

其他解答: