三0 4.
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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![The image contains handwritten mathematical notation on lined paper. The text seems to be solving a quadratic equation for the variable \( y \). The equation is written as follows:
\[ x^2 - 4xy + 4y^2 = 0 \]
Below the equation, there is a note which reads:
\[ \text{obtain } y. \]
This implies that the objective is to solve the given quadratic equation for the variable \( y \).
### Explanation
To solve the equation \( x^2 - 4xy + 4y^2 = 0 \) for \( y \), we can follow these steps:
1. **Recognize the equation:** Notice that the given equation is in the form of a quadratic equation.
2. **Factor the equation:** We can rewrite the equation as:
\[ (x - 2y)^2 = 0 \]
3. **Solve for \( y \):**
\[ x - 2y = 0 \]
\[ x = 2y \]
\[ y = \frac{x}{2} \]
Hence, the solution for \( y \) in terms of \( x \) is \( \boxed{y = \frac{x}{2}} \).
This equation shows that \( y \) is half the value of \( x \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faaa612e4-bb6a-4a7c-9bcb-a4980796bdd1%2F21816232-6914-437a-9761-33172f581b62%2Fjumgilj_reoriented.jpeg&w=3840&q=75)
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