How do you prove brahmagupta Theorem?
To prove that AF = FM, first note that the angles FAM and CBM are equal, because they are inscribed angles that intercept the same arc of the circle. Furthermore, the angles CBM and CME are both complementary to angle BCM (i.e., they add up to 90°), and are therefore equal. Finally, the angles CME and FMA are the same.
What is the formula of area of cyclic quadrilateral?
The area of a cyclic quadrilateral is K=√(s−a)(s−b)(s−c)(s−d) where a, b, c, and d are the four sides of the quadrilateral, and s, the semi perimeter, is defined as s = (1/2)×(a+b+c+d).
Who invented formula for cyclic quadrilateral?
This was derived by the Indian mathematician Vatasseri Parameshvara in the 15th century.
Why is Brahmagupta important?
Introduction. Brahmagupta (ad 628) was the first mathematician to provide the formula for the area of a cyclic quadrilateral. His contributions to geometry are significant. He is the first person to discuss the method of finding a cyclic quadrilateral with rational sides.
What is the formula of perimeter of cyclic quadrilateral?
Solution: Given the measurement of the sides are, 4 cm, 2 cm, 6 cm, and 8 cm. Therefore, the perimeter of a cyclic quadrilateral = 2s = 20.
What do you mean by semiperimeter?
(ˌsɛmɪpəˈrɪmɪtə ) mathematics. half the perimeter of an object or shape.
What is Brahmagupta’s quadratic formula?
Brahmagupta also solves quadratic indeterminate equations of the type a x 2 + c = y 2 ax^{2} + c = y^{2} ax2+c=y2 and a x 2 − c = y 2 ax^{2} – c = y^{2} ax2−c=y2. For example he solves 8 x 2 + 1 = y 2 8x^{2} + 1 = y^{2} 8×2+1=y2 obtaining the solutions. (x, y) = (1, 3), (6, 17), (35, 99), (204, 577), (1189, 3363).
What was Brahmagupta’s biggest contribution to mathematics?
Brahmagupta’s most famous result in geometry is his formula for cyclic quadrilaterals. Given the lengths of the sides of any cyclic quadrilateral, Brahmagupta gave an approximate and an exact formula for the figure’s area, 12.21.
What is cyclic parallelogram called?
Also we know that all the interior angles of a rectangle are equal to 900. Hence, a cyclic parallelogram is a rectangle.
How do you prove the cyclic quadrilateral theorem?
One way we can prove a quadrilateral is cyclic is by demonstrating that an angle created by a diagonal and a side is equal in measure to the angle created by the other diagonal and the opposite side. A rhombus is defined as a quadrilateral with all four sides equal in length.
What is sum of cyclic quadrilateral?
Theorem – The sum of opposite angles of a cyclic quadrilateral is 180° | Class 9 Maths.
What is perimeter of quadrilateral?
The perimeter of a quadrilateral is the total length of its boundary. For example, the perimeter of a quadrilateral ABCD can be expressed as, Perimeter = AB + BC + CD + DA. This means if all the sides of a quadrilateral are known, we can get its perimeter by adding all its sides.
What is meant by the semiperimeter of a triangle?
The semi perimeter of a triangle is half the sum of all its sides. A triangle is a polygon with three sides, three vertices, and three interior angles that add up to 180°. While the perimeter of a triangle is calculated by adding all its sides, the semi perimeter of a triangle is half the value of the perimeter.
What is the use of Brahmagupta’s formula?
Brahmagupta’s formula provides the area A of a cyclic quadrilateral (i.e., a simple quadrilateral that is inscribed in a circle) with sides of length a, b, c, and d as where s is the semiperimeter Note: There are alternative approaches to this proof. The one outlined below is intuitive and elementary, but becomes tedious.
How to find the area of a quadrilateral using Brahmagupta’s formula?
1. If ABCD is a quadrilateral with sides of length a, b, c, and d, such that ABCD is both cyclic and has a circle inscribed in it, then use Brahmagupta’s formula to show that the area of the quadrilateral is 2. Consider Brahmagupta’s formula as one side, say the one of length d wnlog, varies and approaches zero in length.
What is the difference between Bretschneider’s and Brahmagupta’s formula?
Bretschneider’s formula gives a formula for the area of a non-cyclic quadrilateral given only the side lengths; applying Ptolemy’s Theorem to Bretschneider’s formula reduces it to Brahmagupta’s formula. Brahmagupta’s formula reduces to Heron’s formula by setting the side length .
How did Brahmagupta enumerate the properties of zero?
Brahmagupta enumerated the properties of zero as: Discovered the formula to solve quadratic equations. Discovered the value of pi ( 3.162….) almost accurately. He put the value 0.66% higher than the true value. ( 3.14) With calculations, he indicated that Earth is nearer to the moon than the sun.