You have :
Calculate : OB
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 .