Form 4 Maths (angles in circle

圖片參考：http://f20.yahoofs.com/hkblog/ux4rRlOBHhLnw7YkAOw-_1/blog/ap_20100428100423648.jpg?ib_____D8gyKZ5qb



Let P be a point on AE such that OP 丄 AE ,
Let Q be a point on DE such that OQ 丄 DE ,

In △OPE and △OQE ,
OE=OE(common)
ㄥAEF = ㄥDEF(given)
ㄥOPE = ㄥOQE = 90°(knowed)

△OPE ~= △OQE (ASA)

Therefore OP = OQ
EP = EQ......(1)

In△OAP and △ODQ ,
OA = OD (radius)
OP = OQ(proved)
ㄥOPA = ㄥOQD = 90°(knowed)

△OAP~=△ODQ (RHS)

Therefore AP = DQ......(2)

(1) + (2) :

EP + AP = EQ + DQ

AE = DE

In △AEF and △DEF ,

EF = EF (common)
AE = DE(proved)
ㄥAEF = ㄥDEF(given)

△AEF ~= △DEF (SAS)

Therefore AF = DF

Hence arc AF = arc DF

_________________________________________________________
Let M and N be the points on AE and DE respectively such that
OM⊥AE and ON⊥DE.
∆OME≅∆ONE (AAS)
Then,
∆OAM≅∆ODN (RHS)
∠AOF
=180°−∠AOM−∠MOE
=180°−∠DON−∠NOE (corr. sides, ≅∆s)
=∠DOF
∴arc AF = arc FD (eq. angles , eq. arc)

No

2010-04-28 22:15:16 補充：
Unless you add a given that AE= ED