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Question
If the vertices of a triangle be (0, 0), (6, 0) and (6, 8), then its incentre will be ______.
Options
(2, 1)
(1, 2)
(4, 2)
(2, 4)
MCQ
Fill in the Blanks
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Solution
If the vertices of a triangle be (0, 0), (6, 0) and (6, 8), then its incentre will be (4, 2).
Explanation:
Incentre = `((ax_1 + bx_2 + cx_3)/(a + b + c), (ay_1 + by_2 + cy_3)/(a + b + c))`
a = BC = `sqrt((8)^2` = 8
b = CA = `sqrt(36 + 64)` = 10
c = AB = `sqrt((6)^2)` = 6
∴ Incentre = `((8(0) + 10(6) + 6(6))/(8 + 10 + 6), (8(0) + 10(0) + 6(8))/(8 + 10 + 6))`
= `((0 + 60 + 36)/2, (0 + 0 + 48)/24)`
= `(96/24, 48/24)`
= (4, 2)
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Equations of Line in Different Forms - Equations of Internal and External by Sectors of Angles Between Two Lines Co-ordinate of the Centroid, Orthocentre, and Circumcentre of a Triangle
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