AB is a diameter of a circle C(O, r) and radius OD ⊥ AB. If C is any point on arc DB, then find ∠BAD and ∠CAD.
If ∠BAC = 20°, find ∠DAC. 

Given: AB is a diameter of a circle and radius OD ⊥ AB.
∴ ∠BOD = 90° 
∠BOD = 2∠BAD ⇒ ∠BAD = ´ 90°  = 45°
In ΔABD, ∠ADB = 90°  [In semi-circle] ∴ ∠ABD = 90°  - ∠BAD = 90° - 45° = 45° 
Now ∠ABD = ∠ACD ⇒ 45° = ∠ACD 
or ∠ACD = 45° 
Again, ∠BDC = ∠BAC     [Angles in the same segment] ∴ ∠BAC = 20°             [^..^. ∠BDC = 20°] 
Now ∠BAC + ∠CAD = 45° 
⇒ 20° + ∠CAD = 45° 
or ∠CAD = 25°