Question
If P is equidistant from all the sides of the triangle ABC, then a circle drawn with P as the center touching all the sides, then the center of the circle is also called ______.
- Ex-center
- In-center
- Circumcenter
- Centroid
Hint:
We are given a statement. We have to complete the statement by choosing the right option. We will have to see the definitions of all the options. Using that, we can complete the statement.
The correct answer is: In-center
The questions is a about a circle drawn with the point P at its center. The point is equidistant from all sides of the triangle. The circle drawn is touching all the sides of the triangle.
We have to tell what the center of such circle is called.
Centroid is intersection point of the medians of the triangle.
Ex-center is a center of a circle which is lying outside the circle. It is tangent to one of the sides.
In-center is a point equidistant from sides of the triangle. It is the center of the circle inscribed in the triangle. The circle is touching all sides of the triangle.
Circumcenter is point equidistant from vertices of a triangle. It is center of circle passing through all three vertices.
So, the answer we are looking for is in-center.
If P is equidistant from all the sides of triangle ABC. A circle is drawn with P as the center touching all the sides, then the center of the circle is also called the incenter.
For such questions, we should know about the different centers of the circle and triangle.
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