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

(0,0)

Explanation

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).