You have :

Calculate : OB

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- Nov 2nd 2009, 10:28 PMdhiabCircle
**You have :**

**Calculate : OB** - Nov 3rd 2009, 12:24 PMOpalg
__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 .