Brahmagupta and Cyclic Quadrilaterals
This quiz covers Brahmagupta's contributions to geometry, particularly his formula for the area of cyclic quadrilaterals and related theorems.
Questions
What is the name of the Indian mathematician who made significant contributions to geometry?
- Aryabhata
- Brahmagupta
- Bhaskara II
- Varahamihira
What is Brahmagupta's formula for the area of a cyclic quadrilateral?
- $$A = \sqrt{(s-a)(s-b)(s-c)(s-d)}$$
- $$A = \frac{1}{2}ab$$
- $$A = \frac{1}{2}bh$$
- $$A = \frac{1}{2}lw$$
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?
- Brahmagupta's theorem
- Ptolemy's theorem
- Pythagoras' theorem
- Euler's theorem
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?
- Brahmagupta's theorem
- Ptolemy's theorem
- Pythagoras' theorem
- Euler's theorem
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?
- Brahmagupta's theorem
- Ptolemy's theorem
- Pythagoras' theorem
- Euler's theorem
What is the name of the theorem that states that the sum of the angles of a cyclic quadrilateral is 360 degrees?
- Brahmagupta's theorem
- Ptolemy's theorem
- Pythagoras' theorem
- Euler's theorem
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?
- Brahmagupta's theorem
- Ptolemy's theorem
- Pythagoras' theorem
- Euler's theorem
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?
- Brahmagupta's theorem
- Ptolemy's theorem
- Pythagoras' theorem
- Euler's theorem
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?
- Brahmagupta's theorem
- Ptolemy's theorem
- Pythagoras' theorem
- Euler's theorem
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?
- Brahmagupta's theorem
- Ptolemy's theorem
- Pythagoras' theorem
- Euler's theorem
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?
- Brahmagupta's theorem
- Ptolemy's theorem
- Pythagoras' theorem
- Euler's theorem
What is the name of the theorem that states that the diagonals of a cyclic quadrilateral bisect each other?
- Brahmagupta's theorem
- Ptolemy's theorem
- Pythagoras' theorem
- Euler's theorem
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?
- Brahmagupta's theorem
- Ptolemy's theorem
- Pythagoras' theorem
- Euler's theorem
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?
- Brahmagupta's theorem
- Ptolemy's theorem
- Pythagoras' theorem
- Euler's theorem
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?
- Brahmagupta's theorem
- Ptolemy's theorem
- Pythagoras' theorem
- Euler's theorem