Circle

(1)

reflex∠BOD = 2c
∠BOD = 360 - 2c
∠BAD = (360 - 2c)/2 = 180 - c
∠BAD + b + d + reflex∠BOD = 360
180 - c + b + d + 2c = 360
b + c + d = 180
c = 180 - (b + d)


(2)

AH is diameter, such that ∠AEB = ∠AFC = 90
∠AEB + ∠FBH + ∠FAE = ∠AFC + ∠ECH + ∠FAE = 180
90 + ∠FBH + ∠FAE = 90 + ∠ECH + ∠FAE
∠FBH = ∠ECH, thus B, F, E, C are concyclic
statement I is true

as you may draw the figure that while ∠FAH not equal to ∠HAE
so, statement II is false, same as statement III


2014-10-08 08:28:04 補充：
thanks for 少年大大，statement III is true

As CF丄AB, BE丄AC, so, H is the orthocentre of triangle ABC, that is, AD丄BC.
So, III must be true.

In Q2, I and III must be true.

To Maths ( 小學級 3 級)

c,b,d會唔會有d亂呢?....