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A square ABCD is inscribed in a circle of radius R. Another circle is inscribed in ABCD and a square EFGH is inscribed in this circle. The side EF is equal to
- a)R
- b)R / √2
- c)R / 2
- d)R√2
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A square ABCD is inscribed in a circle of radius R. Another circle is ...
►The diameter of the circle becomes the diagonal of the first square.
►So the side AB of the first square is (2)1/2R.
►This side becomes the diameter of the second circle as well as the diagonal of the second square.
►So the side of the second square will be R.
Most Upvoted Answer
A square ABCD is inscribed in a circle of radius R. Another circle is ...
►The diameter of the circle becomes the diagonal of the first square.
►So the side AB of the first square is (2)1/2R.
►This side becomes the diameter of the second circle as well as the diagonal of the second square.
►So the side of the second square will be R.
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A square ABCD is inscribed in a circle of radius R. Another circle is ...
Let's assume the side length of the square ABCD is 2x, and the side length of the square EFGH is 2y.
Since the square ABCD is inscribed in the circle of radius R, the diagonal AC of the square is equal to 2R. Using the Pythagorean theorem, we can find the relationship between the side length of the square and the diagonal:
(2x)^2 + (2x)^2 = (2R)^2
4x^2 + 4x^2 = 4R^2
8x^2 = 4R^2
x^2 = R^2/2
Similarly, we can find the relationship between the side length of the square EFGH and the diagonal EG:
(2y)^2 + (2y)^2 = (2x)^2
4y^2 + 4y^2 = 4x^2
8y^2 = 4x^2
y^2 = x^2/2
Since we know that x^2 = R^2/2, we can substitute this into the equation for y^2:
y^2 = (R^2/2)/2
y^2 = R^2/4
Therefore, the side length of the square EFGH is equal to R/2.
So, the answer is (b) R/2.
Since the square ABCD is inscribed in the circle of radius R, the diagonal AC of the square is equal to 2R. Using the Pythagorean theorem, we can find the relationship between the side length of the square and the diagonal:
(2x)^2 + (2x)^2 = (2R)^2
4x^2 + 4x^2 = 4R^2
8x^2 = 4R^2
x^2 = R^2/2
Similarly, we can find the relationship between the side length of the square EFGH and the diagonal EG:
(2y)^2 + (2y)^2 = (2x)^2
4y^2 + 4y^2 = 4x^2
8y^2 = 4x^2
y^2 = x^2/2
Since we know that x^2 = R^2/2, we can substitute this into the equation for y^2:
y^2 = (R^2/2)/2
y^2 = R^2/4
Therefore, the side length of the square EFGH is equal to R/2.
So, the answer is (b) R/2.
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A square ABCD is inscribed in a circle of radius R. Another circle is inscribed in ABCD and a square EFGH is inscribed in this circle. The side EF is equal toa)Rb)R /√2c)R / 2d)R√2Correct answer is option 'A'. Can you explain this answer?
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A square ABCD is inscribed in a circle of radius R. Another circle is inscribed in ABCD and a square EFGH is inscribed in this circle. The side EF is equal toa)Rb)R /√2c)R / 2d)R√2Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A square ABCD is inscribed in a circle of radius R. Another circle is inscribed in ABCD and a square EFGH is inscribed in this circle. The side EF is equal toa)Rb)R /√2c)R / 2d)R√2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A square ABCD is inscribed in a circle of radius R. Another circle is inscribed in ABCD and a square EFGH is inscribed in this circle. The side EF is equal toa)Rb)R /√2c)R / 2d)R√2Correct answer is option 'A'. Can you explain this answer?.
A square ABCD is inscribed in a circle of radius R. Another circle is inscribed in ABCD and a square EFGH is inscribed in this circle. The side EF is equal toa)Rb)R /√2c)R / 2d)R√2Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A square ABCD is inscribed in a circle of radius R. Another circle is inscribed in ABCD and a square EFGH is inscribed in this circle. The side EF is equal toa)Rb)R /√2c)R / 2d)R√2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A square ABCD is inscribed in a circle of radius R. Another circle is inscribed in ABCD and a square EFGH is inscribed in this circle. The side EF is equal toa)Rb)R /√2c)R / 2d)R√2Correct answer is option 'A'. Can you explain this answer?.
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A square ABCD is inscribed in a circle of radius R. Another circle is inscribed in ABCD and a square EFGH is inscribed in this circle. The side EF is equal toa)Rb)R /√2c)R / 2d)R√2Correct answer is option 'A'. Can you explain this answer?, a detailed solution for A square ABCD is inscribed in a circle of radius R. Another circle is inscribed in ABCD and a square EFGH is inscribed in this circle. The side EF is equal toa)Rb)R /√2c)R / 2d)R√2Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of A square ABCD is inscribed in a circle of radius R. Another circle is inscribed in ABCD and a square EFGH is inscribed in this circle. The side EF is equal toa)Rb)R /√2c)R / 2d)R√2Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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