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X coordinate of incentre of a triangle that has coordinates of midpoint of its sides as (0,1)(1,1) (1,0) is :

X coordinate of incentre of a triangle that has coordinates of midpoint of its sides as (0,1)(1,1) (1,0) is :

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2 Answers

Sunil Kumar FP
askIITians Faculty 183 Points
9 years ago

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thanks and regards
sunil kr
askIItian faculty
Kushagra Madhukar
askIITians Faculty 628 Points
2 years ago
Dear student,
Please find the solution to your problem.
 
The coordinates of the triangle using the mid points of sides are
A : (0, 0)
B : (0, 2)
C : (2, 0)
Let the length of opposite sides be a, b, c.
Length of side of triangle 
a = √[(0 – 2)2 + (2 – 0)2] = 2√2
b = √[(0 – 2)2 + (0 – 0)2] = 2
c = √[(0 – 0)2 + (0 – 2)2] = 2
x co-ordinate of incenter = (axa + bxb + cxc)/(a + b + c)
= 2√2.0 + 2.0 + 2.2/(4 + 2√2)
= 4/(4 + 2√2)
= 2/(2 + √2)
= 2(2 – √2)/(4 – 2)
= 2 – √2
 
Thanks and regards,
Kushagra

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