Question

S1: Incentre of an acute-angled triangle and a right-angled triangle lies inside the triangle.
S2: Circumcentre of an obtuse-angled triangle lies outside the triangle.

• A. Both S1 and S2 are true.
• B. S1 is false and S2 is true .
• C. Both S1 and S2 are false.
• D. S1 is true and S2 is false.

Answer 1

The correct option is A Both S1 and S2 are true.

Incentre of a triangle: The point of intersection of the bisectors of the internal angles of a triangle is called its incentre.
Position of Incentre: For all triangles, Incentre lies inside the triangle.

Circumcentre of a triangle: The point of intersection of the perpendicular bisectors of the sides of a triangle.
Position of circumcentre: Triangle type Position of circumcentre

Acute-angled	Circumcentre lies inside the triangle
Obtuse-angled	Circumcentre lies outside the triangle
Right-angled	Circumcentre lies on the mid-point of hypotenuse