বৃত্ত
All Written Question - (6)
1.
প্রামণ কর যে, কোনো বৃত্তের দুইটি জ্যা পরস্পরকে সমদ্বিখণ্ডিত করলে তাদের ছেদবিন্দু বৃত্তটির কেন্দ্র হবে।
প্রামণ কর যে, কোনো বৃত্তের দুইটি জ্যা পরস্পরকে সমদ্বিখণ্ডিত করলে তাদের ছেদবিন্দু বৃত্তটির কেন্দ্র হবে।
Created: 1 year ago |
Updated: 1 year ago
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Answer
2.
প্রমাণ কর যে, দুইটি সমান্তরাল জ্যা-এর মধ্যবিন্দুর সংযোজক সরলরেখা কেন্দ্রগামী এবং জ্যাদ্বয়ের উপর লম্ব।
প্রমাণ কর যে, দুইটি সমান্তরাল জ্যা-এর মধ্যবিন্দুর সংযোজক সরলরেখা কেন্দ্রগামী এবং জ্যাদ্বয়ের উপর লম্ব।
Created: 1 year ago |
Updated: 1 year ago
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Answer
3.
কোনো বৃত্তের AB ও AC জ্যা দুইটি A বিন্দুগামী ব্যাসার্ধের সাথে সমান কোণ উৎপন্ন করে।
প্রমাণ কর যে, AB = AC
কোনো বৃত্তের AB ও AC জ্যা দুইটি A বিন্দুগামী ব্যাসার্ধের সাথে সমান কোণ উৎপন্ন করে।
প্রমাণ কর যে, AB = AC
Created: 1 year ago |
Updated: 1 year ago
Please, contribute to add answer.
Answer
4.
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)
চিত্রে, O বৃত্তের কেন্দ্র এবং জ্যা AB = জ্যা AC
প্রমাণ কর যে, ∠BAO = ∠CAO
চিত্রে, O বৃত্তের কেন্দ্র এবং জ্যা AB = জ্যা AC
প্রমাণ কর যে, ∠BAO = ∠CAO
Created: 1 year ago |
Updated: 1 year ago
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Answer
5.
কোনো বৃত্ত একটি সমকোণী ত্রিভুজের শীর্ষবিন্দুগুলো দিয়ে যায়। দেখাও যে, বৃত্তটির কেন্দ্র অতিভুজের মধ্যবিন্দু।
কোনো বৃত্ত একটি সমকোণী ত্রিভুজের শীর্ষবিন্দুগুলো দিয়ে যায়। দেখাও যে, বৃত্তটির কেন্দ্র অতিভুজের মধ্যবিন্দু।
Created: 1 year ago |
Updated: 1 year ago
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Answer
6.
দুইটি সমকেন্দ্রিক বৃত্তের একটির AB জ্যা অপর বৃত্তকে C ও D বিন্দুতে ছেদ করে। প্রমাণ কর যে, AC = BD
দুইটি সমকেন্দ্রিক বৃত্তের একটির AB জ্যা অপর বৃত্তকে C ও D বিন্দুতে ছেদ করে। প্রমাণ কর যে, AC = BD
Created: 1 year ago |
Updated: 1 year ago
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Answer
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