Do the bisectors of the angles of a triangle always intersect at a point I ?[br]Can we always draw an inscribed circle from this point?[br][br]Activity :[br]_ Draw a triangle ABC by placing 3 points randomly.[br]_ Draw the angle bisectors of the three vertices of the triangle.[br]_ Place point I at the intersection of the bisectors.[br][br]_ Move points A, B, and C to verify that the bisectors always intersect at point I.[br][br]_ Draw the three lines perpendicular to the sides of the triangle from point I.[br]_Place the points of intersection E, D, and F.[br]_Draw the circle with centre I passing through E.[br][br]_ Move points A, B, and C to verify that the centre thus drawn is still a circle inscribed in the triangle.[br][br]_ Draw segments [EI], [DI], and [FI].[br]In the Algebra pane of Geogebra, note the lengths of these segments.[br][br]_Move points A, B and C, then note the new values of segments [EI], [DI] and [FI].[br][br]_Answer the following questions[br]