Question

In Acute angled triangle the circumcentre is in....
a)inside the triangle
b)outside the triangle
c)undefined​

Answer 1

Answer:

a) inside the triangle

Explanation:

Circumcenter of a triangle refers to a point which is equidistant from all three vertices of the triangle. As it is has equal distance from all the vertices we can draw a circle where all three vertices are on the circumference of the circle thus drawn.

In the attachment, point O is the circumcenter of the triangle XYZ, here OX, OZ and OZ are radius of the circle, OY = OX = OZ.

How to draw circumcenter of the acute angle ∆XYZ.

• Draw a perpendicular bisector of line XY
• Draw perpendicular bisector of line YZ
• Draw a perpendicular bisector of line ZX
• Fnd the point where all three perpendicular bisectors intersect each other, this is the circumcenter of the triangle XYZ.

The ∆XYZ was an acute angle triangle, and we get its circumcenter inside the triangle.

As we know, a point that lies on the perpendicular bisector of a line is equidistant from the both 2 end points of the same line. So, the circumcenter of a triangle will be equidistant from all three vertices. That's why we are able to draw a circle.

if we apply the same construction then we would get to know :

• Circumcentre of an acute angled triangle lies inside the triangle.
• Circumcentre of a right angled triangle lies on its hypotenuse
• Circumcentre of an obtuse angle triangle lies outside the triangle.

Option a) inside the triangle is the correct option.