The problem asks us to calculate the angle between a tangent and a chord (tetiva in Serbian) if the chord divides the circle into two arcs in the ratio 3:7.

1. Problem Description

The problem asks us to calculate the angle between a tangent and a chord (tetiva in Serbian) if the chord divides the circle into two arcs in the ratio 3:

7.

2. Solution Steps

Let the two arcs be $3x$ and $7x$. Since the two arcs together form the entire circle, their sum is $360^\circ$.

So, we have:

$3x + 7x = 360^\circ$

$10x = 360^\circ$

$x = \frac{360^\circ}{10} = 36^\circ$

The two arcs are $3x = 3 \cdot 36^\circ = 108^\circ$ and $7x = 7 \cdot 36^\circ = 252^\circ$.

The angle between the tangent and the chord is half the angle subtended by the chord at the center. Let's consider the smaller arc which has a measure of $108^\circ$. The angle between the tangent and the chord is half of the measure of this arc.

$\text{Angle} = \frac{108^\circ}{2} = 54^\circ$

3. Final Answer

The angle between the tangent and the chord is $54^\circ$.