powered by desmos Find the LENGTH of the arc YX (keep in terms of pi) 10 Y 70° O 10T O 19.4447 O 3.8897T O 70T
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
![**Finding the Length of Arc YX: Understanding Circular Segments**
**Question:**
Find the LENGTH of the arc YX (keep in terms of π).
**Diagram Details:**
The image presents a circle with a radius of 10 units. Point Y and point X are positioned such that angle ∠YX is 70°.
**Solution Approach:**
1. **Identifying the Components:**
- The radius of the circle (r) = 10 units
- The central angle (θ) = 70°
2. **Formula for Arc Length:**
The formula to find the length of an arc (L) is given by:
\[
L = \frac{θ}{360°} \times 2πr
\]
where:
- \(θ\) is the central angle in degrees,
- \(r\) is the radius of the circle.
3. **Substitute the Values:**
\[
L = \frac{70°}{360°} \times 2π \times 10
\]
4. **Simplifying the Equation:**
\[
L = \frac{70}{360} \times 20π
\]
\[
L = \frac{7}{36} \times 20π
\]
\[
L = \frac{140}{36}π
\]
\[
L = \frac{35}{9}π
\]
5. **Final Calculation:**
\[
L ≈ 3.889π
\]
**Answer Choices Provided:**
- 10π
- 19.444π
- 3.889π
- 70π
The calculated arc length of YX is approximately \( 3.889π \).
**Conclusion:**
By applying the formula for arc length and substituting the given values, we determine that the length of arc YX is \(3.889π\).
For more educational resources and learning tips, please explore our website sections on geometry and circle theorems.
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This structure is designed to help students understand and apply the concept of arc length calculation in a clear and step-by-step manner.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34dbf93a-185c-4522-bbbf-f73f18b87311%2F13033935-44a4-4c80-81e2-8f18a225f584%2Fclw9rzu_processed.jpeg&w=3840&q=75)
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