\begin{aligned} & \text { Properties and characteristics of a tangent } \\ & \text { [Two tangents drawn from one point] }\end{aligned}

A circle with center at point $O$ bisects the segment $A O$. Find the angle between the tangents drawn from point $A$.
If the leg of a right triangle is half the hypotenuse, then the angle of the triangle opposite this leg is $30^{\circ}$.

## Solution

Let $B$ be one of the points of tangency. Then, in the right triangle $O B A$, the leg $O B$ is half the hypotenuse $O A$. Therefore, the angle $O A B$ is $30^{\circ}$, and the angle between the tangents is $60^{\circ}$.

![](https://cdn.mathpix.com/cropped/2024_05_06_4fce0705b02fa9e106d4g-04.jpg?height=415&width=560&top_left_y=1296&top_left_x=749)

Answer

$60^{\circ}$.

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