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.
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### Tangent Line Problem
#### Question 1
**Prompt:**
Point B and D are the points of tangency. Find the value of \( x \).
**Diagram Explanation:**
The diagram shows a circle with center \( C \) and two tangents to the circle touching it at points B and D. The tangents form a triangle with the lines extending from these points and intersect at point A outside the circle.
- Line segment \( AB = 3x + 10 \)
- Line segment \( AD = 7x - 6 \)
**Mathematical Representation:**
Since AB and AD are both tangents to the circle from a common external point A, they are equal in length. Hence,
\[
3x + 10 = 7x - 6
\]
Now solve the equation to find \( x \).
*Note: The required response explanation space is provided below the problem statement for students to use.*
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