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.
![### Problem Statement
**Find AB.**
### Diagram Explanation
The diagram shows a trapezoid \(DCAB\) where \(DC\) and \(AB\) are parallel sides. The lengths of the sides are as follows:
- The top base \(DC\) is given as 10 units.
- The middle line segment \(MN\), which is parallel to \(DC\) and \(AB\), is given as 7 units.
The segments are labeled as:
- \(DC = 10\)
- \(MN = 7\)
### Steps to Solve
1. Identify given lengths and relationships between segments.
2. Use properties of trapezoids and similar triangles (if applicable) to find the length of segment \(AB\).
### Solution
Using the properties of midsegments in trapezoids:
\[MN = \frac{1}{2} (DC + AB)\]
Given:
\[MN = 7\]
\[DC = 10\]
Plugging in the values:
\[7 = \frac{1}{2} (10 + AB)\]
Solving for \(AB\):
\[7 \times 2 = 10 + AB\]
\[14 = 10 + AB\]
\[AB = 14 - 10\]
\[AB = 4\]
Thus, the length of \(AB\) is 4 units.
### Conclusion
The length of \(AB\) is 4 units.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F441b01c4-58e7-4b8e-bd53-d84e74382ddb%2F91fabc33-ba1b-4aaf-a265-b2e77800e08f%2Fctdee6_processed.jpeg&w=3840&q=75)
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