The vertices of a triangles are (1,2),(2,3),(3,1) find the centre and radius of its circum circle..
srikrishnacharyulu:
i have one doubt the circle is out side or inside
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given that
A(1,2) ,B(2,3) ,C(3,1)
centroid of the triangle = x₁ + x₂ + x₃ /3 , y₁ + y₂ + y₃ /3
= 1 + 3 + 2 /3 , 2 + 1 + 3 /3
= 6/3 , 6/3
= (2,2)
the radius of the circle = distance of the center of the circle to the out point
= √ (x₁ + x₂)² - (y₁ + y₂)²
= √(2 +3)² - (2 +1)²
= √5² - 3²
= √25 - 9
= √16
= 4 cm
the radius of the circle is 4cm
A(1,2) ,B(2,3) ,C(3,1)
centroid of the triangle = x₁ + x₂ + x₃ /3 , y₁ + y₂ + y₃ /3
= 1 + 3 + 2 /3 , 2 + 1 + 3 /3
= 6/3 , 6/3
= (2,2)
the radius of the circle = distance of the center of the circle to the out point
= √ (x₁ + x₂)² - (y₁ + y₂)²
= √(2 +3)² - (2 +1)²
= √5² - 3²
= √25 - 9
= √16
= 4 cm
the radius of the circle is 4cm
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