Question

Statement 1: The point which is equidistant from three non-collinear points D, E and F is the circumcentre of the ΔDEF.

Statement 2: The incentre of a triangle is the point where the bisector of the angles intersects.

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and Statement 2 is false.

• Statement 1 is false, and Statement 2 is true.

Answer 1

Both the statements are true.

Explanation:

For Statement 1: The circumcentre of a triangle is the point where the perpendicular bisectors of its sides meet. This point is at an equal distance from all three vertices of the triangle. Hence, Statement 1 is correct.

For Statement 2: The incentre of a triangle is the point of intersection of its angle bisectors. It is equally distant from the three sides of the triangle and serves as the centre of the incircle, which is drawn inside the triangle. Therefore, Statement 2 is also correct.