Question

Which statement about an inscribed circle of a triangle is true? 1 The circle does not touch the triangle. 2 The circle touches each side of the triangle exactly once. 3 The circle touches each side of the triangle twice. 4 Each vertex of the triangle is on the circle.

Answer 1

2. The circle touches each side of the triangle exactly once.

Explanation:

The inscribed circle of a triangle is the largest circle that is contained in that triangle. The circle touches each side of the triangle exactly once because at every of these three points the circle is tangent to the corresponding side of the triangle. The center of the circle is called the incenter. The figure below shows inscribed circle of a triangle.