QuestionThe circle below is centred at O . a) Which letter labels a segment of the circle? b) Which letter labels a sector of the circle?
Studdy Solution
STEP 1
What is this asking?
Which labeled part is a segment and which is a sector of the circle?
Watch out!
Don't mix up segments and sectors!
They sound similar, but they're different parts of a circle.
STEP 2
1. Define Segment and Sector
2. Identify the Segment
3. Identify the Sector
STEP 3
Alright, let's break this down!
A **segment** is like a slice of pizza, but instead of cutting straight to the center, we cut with a straight line across the circle, called a *chord*.
The segment is the area between the **chord** and the curved edge, or **arc**, of the circle.
STEP 4
A **sector**, on the other hand, *is* like a normal pizza slice!
It's the area enclosed by **two radii** and the **arc** between them.
Think of it as a slice going straight to the center of the circle.
STEP 5
Looking at our labeled regions, which one looks like our pizza slice cut with a chord?
It's **X**!
Region X is bounded by a chord and an arc, making it a **segment** of the circle.
STEP 6
Now, which region looks like a regular pizza slice with two radii and an arc?
That's **Y**!
Region Y is enclosed by two radii and an arc, making it a **sector** of the circle.
Notice how Z is a triangle, not a sector, because it's formed by two radii and a *chord*, not an *arc*.
STEP 7
a) The segment of the circle is labeled **X**. b) The sector of the circle is labeled **Y**.
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