topic16

Description: This quiz covers topic16 of the Indian Mathematics > Contributions to Geometry subject.
Number of Questions: 15
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What is the name of the Indian mathematician who made significant contributions to geometry?

  1. Aryabhata

  2. Brahmagupta

  3. Bhaskara II

  4. Varahamihira


Correct Option: B
Explanation:

Brahmagupta was an Indian mathematician and astronomer who made significant contributions to geometry, including the development of the Brahmagupta's formula for the area of a cyclic quadrilateral.

What is Brahmagupta's formula for the area of a cyclic quadrilateral?

  1. $$A = \sqrt{(s-a)(s-b)(s-c)(s-d)}$$

  2. $$A = \frac{1}{2}ab$$

  3. $$A = \frac{1}{2}bh$$

  4. $$A = \frac{1}{2}lw$$


Correct Option: A
Explanation:

Brahmagupta's formula for the area of a cyclic quadrilateral is given by $$A = \sqrt{(s-a)(s-b)(s-c)(s-d)}$$, where $$s$$ is the semiperimeter of the quadrilateral and $$a, b, c, d$$ are the lengths of its sides.

What is the name of the theorem that states that the sum of the squares of the diagonals of a cyclic quadrilateral is equal to the sum of the squares of its sides?

  1. Brahmagupta's theorem

  2. Ptolemy's theorem

  3. Pythagoras' theorem

  4. Euler's theorem


Correct Option: A
Explanation:

Brahmagupta's theorem states that the sum of the squares of the diagonals of a cyclic quadrilateral is equal to the sum of the squares of its sides.

What is the name of the theorem that states that the area of a cyclic quadrilateral is equal to the product of its diagonals divided by 2?

  1. Brahmagupta's theorem

  2. Ptolemy's theorem

  3. Pythagoras' theorem

  4. Euler's theorem


Correct Option: A
Explanation:

Brahmagupta's theorem states that the area of a cyclic quadrilateral is equal to the product of its diagonals divided by 2.

What is the name of the theorem that states that the diagonals of a cyclic quadrilateral are perpendicular if and only if the opposite sides are equal?

  1. Brahmagupta's theorem

  2. Ptolemy's theorem

  3. Pythagoras' theorem

  4. Euler's theorem


Correct Option: A
Explanation:

Brahmagupta's theorem states that the diagonals of a cyclic quadrilateral are perpendicular if and only if the opposite sides are equal.

What is the name of the theorem that states that the sum of the angles of a cyclic quadrilateral is 360 degrees?

  1. Brahmagupta's theorem

  2. Ptolemy's theorem

  3. Pythagoras' theorem

  4. Euler's theorem


Correct Option: B
Explanation:

Ptolemy's theorem states that the sum of the angles of a cyclic quadrilateral is 360 degrees.

What is the name of the theorem that states that the product of the diagonals of a cyclic quadrilateral is equal to the sum of the products of its opposite sides?

  1. Brahmagupta's theorem

  2. Ptolemy's theorem

  3. Pythagoras' theorem

  4. Euler's theorem


Correct Option: B
Explanation:

Ptolemy's theorem states that the product of the diagonals of a cyclic quadrilateral is equal to the sum of the products of its opposite sides.

What is the name of the theorem that states that the area of a cyclic quadrilateral is equal to the square root of the product of the areas of its opposite triangles?

  1. Brahmagupta's theorem

  2. Ptolemy's theorem

  3. Pythagoras' theorem

  4. Euler's theorem


Correct Option: B
Explanation:

Ptolemy's theorem states that the area of a cyclic quadrilateral is equal to the square root of the product of the areas of its opposite triangles.

What is the name of the theorem that states that the sum of the squares of the sides of a cyclic quadrilateral is equal to the sum of the squares of its diagonals?

  1. Brahmagupta's theorem

  2. Ptolemy's theorem

  3. Pythagoras' theorem

  4. Euler's theorem


Correct Option: D
Explanation:

Euler's theorem states that the sum of the squares of the sides of a cyclic quadrilateral is equal to the sum of the squares of its diagonals.

What is the name of the theorem that states that the area of a cyclic quadrilateral is equal to the product of its semiperimeter and the radius of its incircle?

  1. Brahmagupta's theorem

  2. Ptolemy's theorem

  3. Pythagoras' theorem

  4. Euler's theorem


Correct Option: D
Explanation:

Euler's theorem states that the area of a cyclic quadrilateral is equal to the product of its semiperimeter and the radius of its incircle.

What is the name of the theorem that states that the sum of the angles of a cyclic quadrilateral is equal to twice the sum of the opposite angles?

  1. Brahmagupta's theorem

  2. Ptolemy's theorem

  3. Pythagoras' theorem

  4. Euler's theorem


Correct Option: D
Explanation:

Euler's theorem states that the sum of the angles of a cyclic quadrilateral is equal to twice the sum of the opposite angles.

What is the name of the theorem that states that the diagonals of a cyclic quadrilateral bisect each other?

  1. Brahmagupta's theorem

  2. Ptolemy's theorem

  3. Pythagoras' theorem

  4. Euler's theorem


Correct Option: D
Explanation:

Euler's theorem states that the diagonals of a cyclic quadrilateral bisect each other.

What is the name of the theorem that states that the area of a cyclic quadrilateral is equal to the square of the radius of its incircle multiplied by the cotangent of half the sum of its opposite angles?

  1. Brahmagupta's theorem

  2. Ptolemy's theorem

  3. Pythagoras' theorem

  4. Euler's theorem


Correct Option: D
Explanation:

Euler's theorem states that the area of a cyclic quadrilateral is equal to the square of the radius of its incircle multiplied by the cotangent of half the sum of its opposite angles.

What is the name of the theorem that states that the sum of the squares of the sides of a cyclic quadrilateral is equal to the sum of the squares of its diagonals plus four times the product of its diagonals?

  1. Brahmagupta's theorem

  2. Ptolemy's theorem

  3. Pythagoras' theorem

  4. Euler's theorem


Correct Option: D
Explanation:

Euler's theorem states that the sum of the squares of the sides of a cyclic quadrilateral is equal to the sum of the squares of its diagonals plus four times the product of its diagonals.

What is the name of the theorem that states that the area of a cyclic quadrilateral is equal to the product of its diagonals divided by 4?

  1. Brahmagupta's theorem

  2. Ptolemy's theorem

  3. Pythagoras' theorem

  4. Euler's theorem


Correct Option: D
Explanation:

Euler's theorem states that the area of a cyclic quadrilateral is equal to the product of its diagonals divided by 4.

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