Question

State wether following statements are true or false. Justify your answer if possible :

(i) Circumcircle and incircle of an quadrilateral triangle can be drawn taking the same center.

(ii) All three sides of a triangle touch its in circle.

(iii) If the given triangle ¡s obtuse, its circumcenter lies on one of its sides.

(iv) The circumcentre of triangle situated inside the triangle when It is an acute triangle.

(v) To construct an incircle of a triangle, we have draw the perpendicular bisector of an two sides of the triangle to obtain the incircle.

Answer 1

(i) True, since the in centre circumcentre and orthocentre of an equilateral triangle are concurrent.

(ii) True, since radius of the in circle of a triangle is equal to the perpendicular drawn from in centre to any of the side of triangle.

(iii) False, only right angled triangle has its circumcentre only on its hypotenuse.

(iv) True.

(v) False, because the in centre of a triangle is the intersecting point of bisectors of any two angles of the triangle.