圆圈部分

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Circles
::圆环

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A circle is the set of all points in the plane that are the same distance away from a specific point , called the center . The center of the circle below is point $\begin{align*}A\end{align*}$ . We call this circle “circle $\begin{align*}A\end{align*}$ ,” and it is labeled $\begin{align*}\bigodot A\end{align*}$ .
::一个圆是平面上所有点的集合,这些点与特定点的距离相同,称为中点。下面圆的中心是 A 点。我们称之为“ A 圈 圈 ” , 它被标为 A 。

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Important Circle Parts
::重要圆环部件

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Radius : The distance from the center of the circle to its outer rim.
::半径:从圆的中心到其外边缘的距离。

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Chord : A line segment whose endpoints are on a circle.
::和弦: 一条线段, 其终点在圆上 。

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Diameter : A chord that passes through the center of the circle. The length of a diameter is two times the length of a radius.
::直径是半径的两倍。

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Secant : A line that intersects a circle in two points.
::secant: 一条将圆交错为两点的线。

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Tangent : A line that intersects a circle in exactly one point.
::切线:一线将圆交错在一个点上。

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Point of Tangency : The point where a tangent line touches the circle.
::切切点: 相切线接触圆圈的点 。

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The tangent ray $\begin{align*}\overrightarrow{TP}\end{align*}$ and tangent segment $\begin{align*}\overline{TP}\end{align*}$ are also called tangents.
::相切的射线“TP”和相切部分“TP”也被称为相切。

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Tangent Circles : Two or more circles that intersect at one point.
::切形圆形:两个或两个以上的圆形在一个点上交叉。

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Concentric Circles : Two or more circles that have the same center, but different radii.
::共心圆圈:两个或两个以上的圆圈具有相同的中心,但不同的弧度。

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Congruent Circles : Two or more circles with the same radius, but different centers.
::共圆:两个或两个以上的圆,半径相同,但中心不同。

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What if you drew a line through a circle from one side to the other that does not pass through the center? What if you drew a line outside a circle that touched the circle at one point? What would you call these lines you drew?
::万一您从一面到另一面画一条线, 从一面到另一面画一条线, 却不通过中间线呢? 如果您在一端触碰圆的圆外画一条线呢? 您如何称呼这些线?

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Examples
::实例

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Example 1
::例1

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Find the parts of $\begin{align*}\bigodot A\end{align*}$ that best fit each description.
::找到ZAA最符合每个描述的部分。

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1. A radius
   ::A半径

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  $\begin{align*}\overline{HA}\end{align*}$ or $\begin{align*}\overline{AF}\end{align*}$
::# # 或 # # # # # h # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #

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2. A chord
   ::和弦和弦

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  $\begin{align*}\overline{CD}, \ \overline{HF}\end{align*}$ , or $\begin{align*}\overline {DG}\end{align*}$
::d, hH, 或

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3. A tangent line
   ::一条正切线

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  $\begin{align*}\overleftrightarrow{BJ}\end{align*}$
::# BJ # # BJ # # BJ # # BJ # BJ # BJ # BJ # BJ # BJ # BJ # BJ # BJ # BJ # BJ # BJ # BJ # BJ # BJ # BJ # BJ # BJ # BJ # BJ # BJ # BJ # BJ #

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4. A point of tangency
   ::某一具体点

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 Point $\begin{align*}H\end{align*}$
::H点点

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5. A diameter
   ::A直径

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  $\begin{align*}\overline{HF}\end{align*}$
::- HF - HF - - - HF - - - - - - - - - - - - - - - - - - - - - - - -

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6. A secant
   ::A 秒数

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  $\begin{align*}\overleftrightarrow{BD}\end{align*}$
::{BD_BD_BD_BD_BD_BD_BD_BD_BD_BD_BD_BD_BD

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Example 2
::例2

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Draw an example of how two circles can intersect with no, one and two points of intersection . You will make three separate drawings.
::绘制一个示例, 显示两个圆圈如何交叉, 交叉点为空、 1 和 2 个。 您将绘制三个独立的图纸 。

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Example 3
::例3

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Determine if any of the following circles are congruent .
::确定以下圆圈中是否有相同圆。

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From each center, count the units to the outer rim of the circle. It is easiest to count vertically or horizontally. Doing this, we have:
::从每个中心, 从每个中心, 计数单位到圆的外边缘。 很容易垂直或水平地计数。 这样做, 我们得到 :

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$$\begin{align*}\text{Radius of} \ \bigodot A & = 3 \ units\\ \text{Radius of} \ \bigodot B & = 4 \ units\\ \text{Radius of} \ \bigodot C & = 3 \ units\end{align*}$$
::A=3 单位Radius= B=4 单位Radius= C=3 单位

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From these measurements, we see that $\begin{align*}\bigodot A \cong \bigodot C\end{align*}$ .
::从这些测量中,我们看到了AAC。

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Notice the circles are congruent. The lengths of the radii are equal.
::注意圆圈是相同的 弧度长度相等

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Example 4
::例4

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Is it possible to have a line that intersects a circle three times? If so, draw one. If not, explain.
::是否可能有一个横线将圆交叉三次? 如果是,请绘制一条。如果没有,请解释。

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It is not possible. By definition, all lines are straight . The maximum number of times a line can intersect a circle is twice.
::不可能。 根据定义, 所有的线条都是直线。 一条线最多能交叉圆的倍数是两次 。

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Example 5
::例5

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Are all circles similar ?
::所有圆圈都相似吗?

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Yes. All circles are the same shape, but not necessarily the same size, so they are similar.
::是的,所有圆圈的形状都一样,但不一定大小相同,因此它们相似。

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Review
::回顾

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Determine which term best describes each of the following parts of $\begin{align*}\bigodot P\end{align*}$ .
::确定哪个术语最能说明 " +P " 的以下每一部分。

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1. $\begin{align*}\overline{KG}\end{align*}$
   :K) (K)
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2. $\begin{align*}\overleftrightarrow{FH}\end{align*}$
   ::芬 芬 华
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3. $\begin{align*}\overline{KH}\end{align*}$
   :KH)
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4. $\begin{align*}E\end{align*}$
   ::英 英 英
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5. $\begin{align*}\overleftrightarrow{BK}\end{align*}$
   ::# BK # # BK # # BK # # BK #
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6. $\begin{align*}\overleftrightarrow{CF}\end{align*}$
   ::CF CF CF CF CF CF CF CF CF CF CF CF CF CF
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7. $\begin{align*}A\end{align*}$
   ::A A A
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8. $\begin{align*}\overline{JG}\end{align*}$
   ::# 城 # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
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9. What is the longest chord in any circle?
   ::圆圈中最长的和弦是什么?

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Use the graph below to answer the following questions.
::使用下图回答下列问题。

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10. Find the radius of each circle.
    ::查找每个圆的半径。
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11. Are any circles congruent? How do you know?
    ::圆圈是否一致?
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12. $\begin{align*}\bigodot C\end{align*}$ and $\begin{align*}\bigodot E\end{align*}$ are externally tangent. What is $\begin{align*}CE\end{align*}$ ?
    ::C和E是外部相切的 CE是什么?
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13. Find the equation of $\begin{align*}\overline{CE}\end{align*}$ .
    
    
    ::找到CE的方程式

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Review (Answers)
::回顾(答复)

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Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

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Resources
::资源