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Chheoki is at a distance of 10 km from Prayagraj Junction on the Howrah–Delhi main line. Trains that bypass Prayagraj Junction and which come from Jabalpur and go towards Mughalsarai usually stop at Chheoki. To reduce the load on the main junction, trains were shifted to Chheoki. [3]
The opening of the Curzon Bridge, across the Ganges, in 1902, linked Prayagraj to regions north of or beyond the Ganges. [5] The Varanasi–Prayagraj City (Rambagh) line was constructed as a metre-gauge line by the Bengal and North Western Railway between 1899 and 1913. It was converted to broad gauge in 1993–94.
Euclid proved that the area of a triangle is half that of a parallelogram with the same base and height in his book Elements in 300 BCE. [1] In 499 CE Aryabhata, used this illustrated method in the Aryabhatiya (section 2.6). [2] Although simple, this formula is only useful if the height can be readily found, which is not always the case.
Prayagraj Division (formerly Allahabad Division) is one of the three railway divisions under the jurisdiction of North Central Railway zone of the Indian Railways. [1] This railway division was formed on 5 November 1951, and its headquarter is located at Prayagraj in the state of Uttar Pradesh of India.
If is the radius of the incircle of the triangle, then the triangle can be broken into three triangles of equal altitude and bases , , and . Their combined area is A = 1 2 a r + 1 2 b r + 1 2 c r = r s , {\displaystyle A={\tfrac {1}{2}}ar+{\tfrac {1}{2}}br+{\tfrac {1}{2}}cr=rs,} where s = 1 2 ( a + b + c ...
The Mumbai–Howrah Mail via Allahabad is called Calcutta Mail between Mumbai and Allahabad, and Mumbai Mail (some still call it by its old name, Bombay Mail) between Allahabad(Now Prayagraj) and Howrah. It is still running for 151 years as the oldest active train on this route covering 2,160-kilometre long (1,340 mi) distance in 37 hours & 30 ...
This formula generalizes Heron's formula for the area of a triangle. A triangle may be regarded as a quadrilateral with one side of length zero. From this perspective, as d approaches zero, a cyclic quadrilateral converges into a cyclic triangle (all triangles are cyclic), and Brahmagupta's formula simplifies to Heron's formula.
There is a method to construct all Pythagorean triples that contain a given positive integer x as one of the legs of the right-angled triangle associated with the triple. It means finding all right triangles whose sides have integer measures, with one leg predetermined as a given cathetus. [13] The formulas read as follows.