Step-by-step explanation:
In ΔAPO and ΔBPO,
( Length of tangents from an external point to a circle are equal)
( Radii of same circle)
( Common side)
∴ ΔAPO = ΔBPO (SSS Congruence) ---------------(1)
Given that, ∠AOP = 64°
∠AOP = ∠BOP [ From (1) ]
⇒∠BOP = 64
Now,
∠BOP + ∠BOD = 180° ( Linear Pair)
∠BOD = 180 - 64 (∵ ∠BOP = 64°)
∴ ∠BOD = 116°
Hope that helps!!
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It took a lot of time to type it!!