Question

A point is equidistant from the sides of an obtuse angle triangle. The point is called ______.

Options

• circumcentre of the triangle

• incentre of the triangle

• centroid of the triangle

• orthocentre of the triangle

Answer 1

A point is equidistant from the sides of an obtuse angle triangle. The point is called incentre of the triangle. 

Explanation:

Let ABC be the obtuse triangle.

Steps of construction:

1. Draw angle bisectors AX, BY and CZ of the interior angles A, B and C of a triangle.
2. Let the angle bisectors meet at point I.

We know that,

Locus of a point equidistant from two intersecting lines is the bisector of the angles between the lines.

∴ BY is equidistant from AB and BC

∴ AX is equidistant from AB and AC

∴ CZ is equidistant from AC and BC

∴ The point (incenter) joining AX, BY and CZ will be equidistant from all the three sides of the triangle.