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Which of the following is equidistant fr...

Which of the following is equidistant from the vertices of a triangle ?

A

circumcentre

B

centroid

C

orthocentre

D

incentre

Text Solution

AI Generated Solution

The correct Answer is:
To determine which point is equidistant from the vertices of a triangle, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Triangle and its Vertices**: - Consider a triangle with vertices labeled as A, B, and C. 2. **Identify the Concept of Equidistance**: - A point that is equidistant from the vertices of a triangle is a point that has the same distance to each of the triangle's vertices. 3. **Introduce the Circumcenter**: - The point that is equidistant from all three vertices of a triangle is known as the **Circumcenter**. 4. **Visualize the Circumcenter**: - To find the circumcenter, you can draw the perpendicular bisectors of each side of the triangle. The point where these bisectors intersect is the circumcenter. 5. **Conclusion**: - Therefore, the circumcenter is the point that is equidistant from the vertices A, B, and C of the triangle. ### Final Answer: The point that is equidistant from the vertices of a triangle is the **Circumcenter**. ---
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Knowledge Check

  • What is the total number of points in the plane of triangle ABC which is equidistant from the vertices of the triangle?

    A
    0
    B
    1
    C
    2
    D
    3

  • The coordinates of the point which is equidistant from the three vertices of the triangle AOB as shown in the figure is

    A
    `(x,y)`
    B
    `(y,x)`
    C
    `((x)/(2),(y)/(2))`
    D
    `((y)/(2),(x)/(2))`

  • A point P lying inside a triangle is equidistant from the vertices of the triangle. Then the triangle has P as its

    A
    Centroid
    B
    Incentre
    C
    Orthocentre
    D
    Circumcentre

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