Answer:
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Explanation:
To find the ratio of the slope to the base of an isosceles triangle, we can use the fact that the slope of a line is given by the ratio of the vertical change to the horizontal change. Let's denote the slope of the triangle as m, the base as b, and the height as h. Then, the ratio of the slope to the base can be expressed as m/b.
The given information states that the point of contact of the inscribed circle divides the slope by the ratio 7:5 from the side of the vertex. This implies that the ratio of the heights of the two smaller triangles formed by the point of contact of the inscribed circle is 7:5.
Using the properties of similar triangles, we can express the ratio of the slope to the base as the ratio of the heights to the base. Therefore, the ratio of the slope to the base is 7:5.
This conclusion is based on the fact that the ratio of the slopes of two similar triangles is equal to the ratio of their corresponding sides. Therefore, the ratio of the slope to the base of the isosceles triangle is 7:5.