$\left[\begin{array}{l}{[\text { The inscribed angle is half the central angle }} \\ {[\quad \text { Properties and characteristics of tangents }}\end{array}\right]$

$A B$ and $A C$ are two chords forming angle $B A C$, which is equal to $70^{\circ}$. Tangents are drawn through points $B$ and $C$ until they intersect at point $M$. Find $\angle B M C$.
$$
\cup B C=2 \angle B A C=140^{\circ}, \angle B M C=180^{\circ}-2 \angle B A C=180^{\circ}-140^{\circ}=40^{\circ}
$$

?C

The angle between the tangents drawn from a point to a circle complements the corresponding central angle to $180^{\circ}$.

![](https://cdn.mathpix.com/cropped/2024_05_06_4fce0705b02fa9e106d4g-04.jpg?height=391&width=900&top_left_y=-1&top_left_x=585)

## Answer

$40^{\circ}$.