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Question

Find the incentre of the triangle whose vertices are A(1, 2, 3), B(1, 5, 3) and C(5, 2, 3).

A
(3,3,3)
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B
(3,2,3)
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C
(2, 3, 3)
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D
(3,2,2)
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E
(2,2,3)
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Solution

The correct option is C (2, 3, 3)


We saw that incentre of the above triangle is given by
l=(ax1+bx2+cx3a+b+c,ay1+by2+cy3a+b+c,az1+bz2+cz3a+b+c).....(1)
a, b and c are lengths of sides.
a is the distance between B(1, 5, 3) and C(5, 2, 3).
Using distance formula, we get a = (15)2+(52)2+(33)2
= 5 units
SImilarly we get b = 4 and c = 3 units
Substituting a = 5, b = 4 , c = 3 and the coordinates of A, B and C in (1), we get
l=(5(1)+4(1)+3(5)5+4+3,5(2)+4(5)+3(2)5+4+3,5(3)+4(3)+3(3)5+4+3)
=(2,3,3)

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