go off on a tangent
collocation突然离题；跑题
When she mentioned his ex, he went off on a tangent about his new job.
她一提到他的前任，他就开始跑题聊他的新工作。
切线
先理解核心含义，再看它在真实句子里的用法。
切线
a line that touches a curve at only one point
We were discussing the budget when she suddenly went off on a tangent about her vacation.
我们正在讨论预算，她突然跑题说起她的假期。
与曲线在一点相切而不交叉的直线
A straight line touching a curve at a single point without crossing it there.
角的函数,给出正弦与余弦的比值,符号:tan, tg
A function of an angle that gives the ratio of the sine to the cosine, in either the real or complex numbers. Symbols: tan, tg.
与主要话题几乎无关但有共同点的话题
A topic nearly unrelated to the main topic, but having a point in common with it.
两条或多条线或边之间的视觉交互,常常是艺术家未预料到的关系
A visual interaction between two or more lines or edges that creates a perceived relationship between them, often in a way that the artist did not intend.
His speech started well, but he kept going off on tangents that confused the audience.
他的演讲开头很好，但他一直跑题，让听众感到困惑。
Please avoid tangents during the meeting so we can finish on time.
会议期间请避免跑题，这样我们才能按时结束。
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突然离题；跑题
When she mentioned his ex, he went off on a tangent about his new job.
她一提到他的前任，他就开始跑题聊他的新工作。
切线
The tangent line touches the circle at exactly one point.
切线恰好与圆相交于一点。
正切函数
In trigonometry class, we learned to graph the tangent function.
三角函数课上，我们学习了绘制正切函数的图像。
突然岔开话题；偏离主题
We were discussing the budget when he went off on a tangent about his vacation.
我们正在讨论预算，他突然岔开话题说起他的假期。
突然转换话题；跑题
The speaker kept flying off at a tangent and never answered the question.
演讲者不停地跑题，始终没有回答问题。
Use tangent naturally, then get feedback on meaning, tone, grammar, and phrasing.
Revisit a common error or keep this word in your review list.
联想：'tangent' 开头是 tan（正切符号），几何里切线一触即离；聊着聊着跑题也像从主线“切”出去。记住 tan 就能想起“切线/正切/跑题”三种意思。
语域：formal 常见场景：geometry class、math textbook、academic paper 作“切线”解时，通常用于数学或几何等正式语境，多出现在教科书、课堂或论文中，属于专业术语，语气正式。若指“跑题”等义项，则可能更口语化。
数学中指导数或切线；引申义指突然转变话题，常用短语 go off on a tangent.
Dictionary facts from ECDICT, WIKTIONARY, WORDNET.