Construction

Draw a (blue) circle with center , radius and a diameter . Let be a point on such that .

Step 1: Draw a (red) circle with diameter and center , the midpoint of . Let be on such that .

Step 2: Let intersect at .

Step 3: Let be symmetric to across .

Step 4: Draw the triangle .

Verification

Let and .

Let be symmetric to across . Let be the intersection of and .

The angle between the angle bisector from and the altitude from is ; also, .

So is the bisector of the angle at . Since , and , , so .