The vertex.
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It really depends on the angle. If the angle is at the point where the two equal sides intersect then you can divide the triangle into two equal parts (forming a right angle with the base), divide the angle by two, then use the following equation(side*arccos(your angle/2))*((side*arcsin(your angle/2)))if the angle is not where the two equal sides intersect then you can divide the triangle into two equal parts (from the point where the two equal sides intersect down to a right angle with the base) then use the following equation.(side*arcsin(your angle)*(side*arccos(your angle))
It is the vertex. The one at which you can have the two points located together! Happy to help!
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle-apex
vertex
vertex