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A circle passes through the vertex A of an equilateral triangle ABC and is tangent to BC at its midpoint .

Find the ratio in which the circle divides each of the sides AB and AC?

Does the line joining the vertex A and the midpoint of BC will be perpendicular to BC? How can i achieve this? Thanks in advance.

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    http://en.wikipedia.org/wiki/Secant-tangent_theorem2012-04-05

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