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Q: Do the perpendicular bisectors of a triangle always sometimes or never intersect on the triangle?

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The three ANGLE bisectors of a triangle also bisect the sides, and intersect at a point INSIDE the triangle. The angle bisectors are not necessarily perpendicular to them. The perpendicular bisectors of the sides can intersect in a point either inside or outside the triangle, depending on the shape of the triangle.

The perpendicular bisectors of the sides of a triangle intersect at its circumcentre.

Since the intersection of the perpendicular bisectors of a triangle is the center of the inscribed circle (we call it the centroid of a triangle), the answer is no.

circumcenter

The three perpendicular bisectors (of the sides) of a triangle intersect at the circumcentre - the centre of the circle on which the three vertices of the triangle sit.

a right triange

Only at the midpoint of the hypotenuse.

The point where the perpendicular bisectors of the three sides of the triangle intersect

They are not. The perpendicular bisectors of a triangle, for example, intersect at the orthocentre of the triangle. So perpendicular lines can be intersecting and conversely.

Circumcenter

yes, because perpendicular lines always intersect. all lines intersect unless they are parallel or on separate planes (skew)

sf sf sf

The angle bisectors always intersect inside the triangle. (This is not true for altitudes and right bisectors.)

Equilateral triangles have 3 perpendicular bisectors

equilateral triangle

all three perpendicular bisectors elongate to meet at the incenter of the triangle.

circumcenter

The perpendicular bisector of ANY chord of the circle goes through the center. Each side of a triangle mentioned would be a chord of the circle therefore it is true that the perpendicular bisectors of each side intersect at the center.

No, never.

inside the triangle ;) hope this helps!!

circumcenter

circumcenter

It is the circumcentre.

Yes.

It is the incentre.