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# The Problem!

Let ABC be a triangle in which AB = AC and let I be its in-centre. Suppose BC = AB + AI. Find ∠BAC.

• For any triangle ABC, $$\frac{\sin A}{a} = \frac{\sin B } {b} = \frac {\sin C }{c}$$.
• Addendo: If $$\frac{a}{b} = \frac{c}{d}$$ then each of these ratios are equal to $$\frac {a+b}{c+d}$$
• $$\sin (90 + \theta ) = \cos \theta$$
• $$\cos ^2 2 \theta = 2 \cos ^2 \theta -1 = \cos ^2 \theta – \sin ^2 \theta$$

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#### RMO 2009

RMO 2009 problems, discussions and other resources. Read more