Track / Stage 4 / 49 of 340 #309 of 1964

Problem 309

AMC 12 late, AIME early

Geometry Difficulty 4.6 Find the answer

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) $45^{\circ}$

(D) $55^{\circ}$

(E) none of the above.

Your answer

Multiple choice: answer with the letter of the option you want.

Official solution

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 $B \hat{C} D=180^{\circ}-90^{\circ}-35^{\circ}=55^{\circ}$ .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.