Ab Is Diameter Of Circle With Centre O And Radius Od Is Perpendicular To Ab

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.

Answers:

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˚