AB is a diameter of a circle with centre O and radius OD is perpendicular to AB. If C is any point on arc DB, find ∠BAD and ∠ACD.
Since, chord BD makes ∠BOD at the centre and ∠BAD at A.
∴ ∠BAD = ½ ∠BOD = ½ × (90˚) = 45˚
Similarly, chord AD makes ∠AOD at the centre and ∠ACD at C.
∴ ∠ACD = ½ ∠AOD
= ½ × (90˚) = 45˚
Thus, ∠BAD = ∠ACD = 45˚