Track / Stage 4 / 157 of 340 #417 of 1964

Problem 417

AMC 12 late, AIME early

Geometry Difficulty 4.7 Find the answer

Given the circle $x^{2}+y^{2}=1$ and the line $y=2 x+m$ intersect at $A$ and $B$ , and $O A$ and $O B$ form angles $\alpha, \beta$ with the positive direction of the $x$ -axis, then $\sin (\alpha+\beta)=$ $\qquad$

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

$-\frac{4}{5} ;$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.