Question

in a triangle ABC a=5,b=4,c=3,G is centroid of triangle ABC circum radius of GAB is ​

Answer 1

Circum Radius of GAB  =  5√13/12   if in  triangle ABC a=5,b=4,c=3, G is centroid of triangle ABC

Step-by-step explanation:

Δ ABC a=5,b=4,c=3,

5² =4² + 3²

=> a² = b² + c²

=> Δ ABC  is right angle Triangle

Let say  B is (0, 0)  , A ( 0 , 3)  & C ( 4, 0)

=> G  = (4/3 , 3/3)  = (4/3 , 1)

GB = √(4/3 -0 )² + (1 - 0)²  = 5/3

GA = √(4/3 -0 )² + (1 - 3)²  = √52/3  = 2√13 / 3

AB = 3

Circum Radius of GAB =  GA * GB * AB / (4 * Area of ΔGAB)

Area of GAB = (1/3) Area of Δ ABC = (1/3) * ((1/2) * 3 * 4)  = 2

Circum Radius of GAB  =  (2√13 / 3) * (5/3) * 3  /(4 * 2)

= 5√13/12

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