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The vertices of the triangle are A (-36,7) ,B (20,7) and C (0,-8)
a = BC = √(0-20)² + (-8-7)²
= √(-20)² + (-15)²
= √400+225
= √625
= √25 x 25
= 25
b = CA = √(36-0))² + (7-(-8))²
= √(36)² + (7+8)²
= √1296 + 15²
= √1296+225
= √1521
= √39 x 39
= 39
c = AB = √(20-(-36))² + (7-7)²
= √(20+36)² + (0)²
= √56²
= √56 x 56
= 56
Incentre I of the triangle is
[(ax₁ + bx₂ + cx₃)/(a+b+c),(ay₁ + by₂ + cy₃)/(a+b+c)]
x₁ = -36 y₁ = 7 x₂ = 20 y₂ = 7 x₃ = 0 y₃ = -8
a = 25 b = 39 c = 56
= [25(-36)+39(20)+56(0)/(25+39+56),25(7)+39(7)+56(-8)/(25+39+56)]
= [(-900+780+0)/(120),(175+273-448/(120)]
= [(-120)/120,(448-448)/120]
= (-1,0)
So the incentre is (-1,0)
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