(1), OP is the waist, and o is the vertex.

Draw a circle with O as the center, the length of OP as the radius, and the intersection line A as two points.

Two isosceles triangles can be obtained by connecting p and these two points respectively.

(2), OP is the waist and P is the vertex.

Draw a circle with P as the center and the length of PO as the radius. It intersects with the straight line A at one point, and the other point is the O point.

Connect p with this point to get an isosceles triangle.

(3), OP is the bottom.

Perpendicular bisector, who is the line segment OP, intersects with the straight line A at a point, and connects this point with the point P to obtain an isosceles triangle.

There are at most four such triangles.

Depending on the angle, there may be overlap.

When the angle between OP and straight line A is 60 degrees, or 90 degrees, there are only two.

If it is arbitrary, it is two or four.

Recommend it! Ask me directly if you have any questions.