Question

Please help!

Answer 1

Step-by-step explanation:

In ΔAPO and ΔBPO,

$AP = BP$      ( Length of tangents from an external point to a circle are equal)

$OA = OB$      ( Radii of same circle)

$OP = OP$      ( 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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