Find the incentre of a triangle formed by the lines `x "cos" (pi)/(9) + y "sin" (pi)/(9) = pi, x "cos" (8pi)/(9)+ y "sin" (8pi)/(9) = pi " and " x "co

Question

Find the incentre of a triangle formed by the lines `x "cos" (pi)/(9) + y "sin" (pi)/(9) = pi, x "cos" (8pi)/(9)+ y "sin" (8pi)/(9) = pi " and " x "co

Find the incentre of a triangle formed by the lines `x "cos" (pi)/(9) + y "sin" (pi)/(9) = pi, x "cos" (8pi)/(9)+ y "sin" (8pi)/(9) = pi " and " x "cos" (13pi)/(9) + y "sin" ((13pi)/(9)) = pi.`

Monjur Alahi

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2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - (0,0)
Incentre of the triangle is the point which is equidistant from all the sides of triangle.
Clearly, distance of origin from all the three given lines is `pi`.
Also, (0,0) is interior point of triangle which can be verified by drawing lines on the plane.
So, incentre of the triangle is (0,0).

23 views Answered 2023-02-05 15:29