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.
In the
![**Intersecting Chords in a Circle**
This diagram illustrates two chords intersecting inside a circle.
- **Chord AB** and **Chord CD** intersect at point **E** within the circle.
Key points and measurements:
- **A**, **B**, **C**, and **D** are points on the circumference of the circle.
- **E** is the intersection point of chords **AB** and **CD**.
- The segment from point **A** to point **E** (AE) measures 9 units.
- The segment from point **E** to point **B** (EB) measures 4 units.
This demonstrates a fundamental geometric property: when two chords intersect inside a circle, the products of the lengths of the segments of each chord are equal. This property can be summarized as:
\[ AE \times EB = DE \times EC \]
Based on the given lengths:
\[ AE = 9 \quad \text{and} \quad EB = 4 \]
So:
\[ 9 \times 4 = DE \times EC \]
This property aids in solving many geometric problems involving circles and their chords.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33ef17cf-3057-4313-84bc-763127c3429d%2F68529f8e-c5bf-44f7-8e43-1ac60f3fe193%2Fxnw222s_processed.png&w=3840&q=75)
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