Step 1.By Pythagoras' theorem, . Let M be the midpoint of AC. Then .

Step 2.OM is perpendicular to AC. By Pythagoras' theorem in the triangle OAM, .

Step 3.Write for the angle OAB, and for the angle BAC. From triangle OAM, and . From triangle ABC, and .

Step 4.Therefore (using the trig formula for the cosine of the difference of two angles).

Step 5.Now apply the cosine rule in triangle OAB to find .