Question

The length of the diameter of the circum circle of the triangle with vertices (a, 0), (a, b) and (0, b) is

Answer 1

Answer:

2× root (a^2 +b^2)

Step-by-step explanation:

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Answer 2

Given :  triangle with vertices (a, 0), (a, b) and (0, b)

To Find :   length of the diameter of the circum circle of the triangle

Solution:

Let say circum circle of triangle is (x , y )

Distance from Each vertex = Circum radius

=> (x - a)² + ( y - 0)²  =   (x - a)² + ( y - b)² =  (x - 0)² + ( y - b)²

(x - a)² + ( y - 0)²  =   (x - a)² + ( y - b)²

=> y²  = y² - 2by  + b²

=> b² = 2by

=>  y = b/2

(x - a)² + ( y - b)² =  (x - 0)² + ( y - b)²

=> x² - 2ax  + a² = x²

=> 2ax = a²

=> x = a/2

(a/2 , b/2)  is center  

Hence Radius =  √(a-a/2)²+ ( b -b/2)²

= (1/2) √a² + b²

Diameter = 2 * radius = √a² + b²

√a² + b²   is The length of the diameter of the circum circle of the triangle with vertices (a, 0), (a, b) and (0, b)

Another way , show that  its a right angle triangle

and hypotenuse act as Diameter of circumcircle

Length of hypotenuse = √a² + b²

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