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