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.`

Find the incentre of a triangle formed by the lines `x "cos" (pi)/(9)

1.	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.`
Answer» 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).

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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.`

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