Which of the following is a FALSE statement?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. The angle formed by any side at the incentre is always 90° more than the angle at the opposite vertex.
Concept used:
Circumcentre: The intersection point of two perpendicular bisectors of a triangle is the circumcentre of the triangle.
The circumcenter is also the center of the circle passing through the three vertices, which circumscribes the triangle.
Euclidean geometry: The three interior angle bisectors of a triangle meet at a single point. The incenter lies at equal distances from the three line segments forming the sides of the triangle and also from the three lines containing those elements.
The centroid of a triangle divides the medians into segments in the ratio of 2 : 1, where the centroid is closer to the midpoint of the side (where the median intersects the side).
So,
The angle formed by any side at the incentre is always 90° more than half of the angle opposite to the side.