Question

The coordinates of the point which is equidistant from the vertices of the triangle formed by the points O(0, 0), A(a, 0) and B(0, b), are ______.

Answer 1

The coordinates of the point which is equidistant from the vertices of the triangle formed by the points O(0, 0), A(a, 0) and B(0, b), are `underlinebb((a/2"," b/2))`.

Explanation:

The point equidistant from the three vertices is the circumcenter (intersection of perpendicular bisectors).

Midpoint of OA is `(a/2, 0)`; its perpendicular bisector is the vertical line `x = a/2`.

Midpoint of OB is `(0, b/2)`; its perpendicular bisector is the horizontal line `y = b/2`.

Their intersection is `(a/2, b/2)`, which is equidistant from O(0, 0), A(a, 0) and B(0, b).