3[ Two tangents drawn from one point ]

In an isosceles triangle, the lateral side is divided by the point of tangency of the inscribed circle in the ratio 7:5 (starting from the vertex). Find the ratio of the lateral side to the base.

#
Tangent segments drawn from a single point to a circle are equal to each other.

## Solution

Since the triangle is isosceles, and the segments of the tangents drawn from one point are equal to each other, the base contains 10 parts, and the lateral side contains 12.

![](https://cdn.mathpix.com/cropped/2024_05_06_4fce0705b02fa9e106d4g-05.jpg?height=411&width=486&top_left_y=2347&top_left_x=795)

Answer

$6: 5$.