Question

Which of the following is true about incircle of a triangle?

• A. The incircle of a triangle is the largest circle that fits in a triangle.
• B. Its center is the incenter.
• C. Its center is the one point inside the triangle that is equidistant from all sides of the triangle.
• D. None of these

Answer 1

Answer: (A), (B), (C)

The correct options are
A Its center is the incenter.
B The incircle of a triangle is the largest circle that fits in a triangle.
C Its center is the one point inside the triangle that is equidistant from all sides of the triangle.

As shown in the figure incircle is the largest circle that can be inscribed in a triangle.

So $A$ is correct.

Its centre is called incentre . $O$ is the incentre in the figure.

So $B$ is also correct.

All the sides are at a constant distance $r$ from the centre.

So $C$ is also correct.