Construction

Step 1: Draw a horizontal line of length and the foot of the altitude from . Measure out a point so that , so that is the midpoint of .

Step 2: Draw a vertical line through .

Step 3: Draw a circle with center so that the central angle .

Step 4: Let the intersections of and , if they exist, be and . Join , , and .

Then either of the two triangles or is a solution.

Step 5: Draw the triangle (dashed line).

Verification

Let and .

Consider the triangle (the verification for the triangle is similar). Because is the right bisector of , , so the angle . But this angle subtends the chord and is half of the central angle over , which is . So .