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In Δ A B C , If a2 + b2 + c2 = 8 R2 , then the triangle is
- a)Right angled
- b)Isosceles
- c)Equilateral
- d)None
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In Δ A B C , If a2 + b2 + c2 = 8 R2, then the triangle isa)Right...
Right Angled Triangle Condition:
There is a well-known theorem in geometry called the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, if a, b, and c are the sides of a right-angled triangle with hypotenuse c, then a^2 + b^2 = c^2.
Given Condition:
In this problem, we are given that a^2 + b^2 + c^2 = 8R^2, where R is the circumradius of the triangle ΔABC. We know that in a right-angled triangle, a^2 + b^2 = c^2. Therefore, if we have a^2 + b^2 + c^2 = 8R^2, it implies that c^2 = 8R^2. This means that the triangle satisfies the condition of a right-angled triangle.
Conclusion:
Hence, based on the given condition a^2 + b^2 + c^2 = 8R^2, we can conclude that the triangle ΔABC is a right-angled triangle. This is because the sum of the squares of the lengths of the sides a and b is equal to the square of the length of the hypotenuse c, which is a characteristic property of right-angled triangles.
There is a well-known theorem in geometry called the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, if a, b, and c are the sides of a right-angled triangle with hypotenuse c, then a^2 + b^2 = c^2.
Given Condition:
In this problem, we are given that a^2 + b^2 + c^2 = 8R^2, where R is the circumradius of the triangle ΔABC. We know that in a right-angled triangle, a^2 + b^2 = c^2. Therefore, if we have a^2 + b^2 + c^2 = 8R^2, it implies that c^2 = 8R^2. This means that the triangle satisfies the condition of a right-angled triangle.
Conclusion:
Hence, based on the given condition a^2 + b^2 + c^2 = 8R^2, we can conclude that the triangle ΔABC is a right-angled triangle. This is because the sum of the squares of the lengths of the sides a and b is equal to the square of the length of the hypotenuse c, which is a characteristic property of right-angled triangles.
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In Δ A B C , If a2 + b2 + c2 = 8 R2, then the triangle isa)Right angledb)Isoscelesc)Equilaterald)NoneCorrect answer is option 'A'. Can you explain this answer?
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In Δ A B C , If a2 + b2 + c2 = 8 R2, then the triangle isa)Right angledb)Isoscelesc)Equilaterald)NoneCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In Δ A B C , If a2 + b2 + c2 = 8 R2, then the triangle isa)Right angledb)Isoscelesc)Equilaterald)NoneCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In Δ A B C , If a2 + b2 + c2 = 8 R2, then the triangle isa)Right angledb)Isoscelesc)Equilaterald)NoneCorrect answer is option 'A'. Can you explain this answer?.
In Δ A B C , If a2 + b2 + c2 = 8 R2, then the triangle isa)Right angledb)Isoscelesc)Equilaterald)NoneCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In Δ A B C , If a2 + b2 + c2 = 8 R2, then the triangle isa)Right angledb)Isoscelesc)Equilaterald)NoneCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In Δ A B C , If a2 + b2 + c2 = 8 R2, then the triangle isa)Right angledb)Isoscelesc)Equilaterald)NoneCorrect answer is option 'A'. Can you explain this answer?.
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