11-3. Point $O$ is the center of the circle. What is the value of angle $x$ in degrees?

![](https://cdn.mathpix.com/cropped/2024_05_06_a41f3cf8d340fa431bbcg-30.jpg?height=480&width=870&top_left_y=1999&top_left_x=593)
Answer: 58.

Solution. Angle $ACD$ is a right angle since it subtends the diameter of the circle.

![](https://cdn.mathpix.com/cropped/2024_05_06_a41f3cf8d340fa431bbcg-31.jpg?height=537&width=894&top_left_y=388&top_left_x=587)

Therefore, $\angle CAD = 90^{\circ} - \angle CDA = 48^{\circ}$. Also, $AO = BO = CO$ as they are radii of the circle, so $\angle OCA = \angle ACO = 48^{\circ}$ and $x = \angle OBC = \angle OCB = 48^{\circ} + 10^{\circ} = 58^{\circ}$.