10) Suppose that, in the circle in the figure, the angle $B A C$ is $35^{\circ}$. Let $C D$ be the diameter passing through $C$, what is the value of $B \widehat{C} D$?

(A) $35^{\circ}$

(B) $45^{\circ}$

(C) $50^{\circ}$

(D) $55^{\circ}$

(E) none of the above.

![](https://cdn.mathpix.com/cropped/2024_04_17_b5d519ff6c1a8005abb1g-1.jpg?height=354&width=395&top_left_y=1218&top_left_x=2376)
10) The answer is $(D)$

Indeed, $C \hat{B} D=90^{\circ}$ and $B \hat{D} C=35^{\circ}$, since it subtends the same arc as $B \hat{A} C$, therefore $B \hat{C} D=180^{\circ}-90^{\circ}-35^{\circ}=55^{\circ}$.