প্রদত্ত চিত্রে, PA এবং PB হল O কেন্দ্র বিশিষ্ট বৃত্তের স্পর্শক, এবং ∠APB = 54° হলে, ∠OBA = ?

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SSC CGL 2022 Tier-I Official Paper (Held On : 12 Dec 2022 Shift 4)
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  1. 27°
  2. 40°
  3. 30°
  4. 35°

Answer (Detailed Solution Below)

Option 1 : 27°
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প্রদত্ত:

PA এবং PB হল O কেন্দ্র বিশিষ্ট বৃত্তের স্পর্শক, এবং ∠APB = 54°

গণনা:

আমরা জানি যে ব্যাসার্ধ এবং স্পর্শক তাদের ছেদবিন্দুতে পরস্পর লম্ব হয়।

অতএব,

∠PAO = ∠PBO = 90°

সুতরাং,

∠AOB = 360 - 54 - 180

⇒ 126°

আবার, AO = OB = ব্যাসার্ধ

অতএব, ∠OAB = ∠OBA = 54/2

⇒ 27°

∴ নির্ণেয় উত্তর হল 27°

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