Question

The figure shows an isosceles triangle ABC with <B = <C. The bisector of angle B intersects the side AC at the point P. Suppose that the base BC remains fixed but the altitude AM of the triangle approaches 0, so A approaches the midpoint M of BC. What happens to P during this process? Does it have a limiting position? If so, find it. Try to sketch the path traced out by P during this process. Then find an equation of this curve and use this equation to sketch the curve.

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