Maths

Question 1
CBD=angle DBE=angle EBA (equal arcs, equal angles)
Why? {{given equal arcs , conclusion equal angles
example if arc CD = 2 arc AB
arc CD /arc AB = x/20ﾟ (angles are prop.to arcs)
x = 40ﾟ }}
Question 2
angle ABE = angle EBD = angle DBC (given)
AE = ED = DC (equal angles, equal chords )
Question 3
(HKCEE 1995 Q14(a)(ii))

∠ PRQ = ∠ APQ (∠ in alt. segment)
yes, ∠ AQP = ∠ PRQ or ∠ PRQ = ∠ AQP (∠ in alt. segment)
但問題不是求∠ AQP = ∠ PRQ 問題是求∠ PRQ = ∠ APQ
此外∠ APQ = ∠ AQP
因為 AP = AQ (tangent prop.)
∠ APQ = ∠ AQP (base ∠s, isos.△)