The Angles Formed by Chords, Secants, and Tangents Calculator is a useful tool for determining the angles formed by these elements in a circle. It helps users calculate the angle between a chord and a tangent or between a secant and a tangent, providing valuable insights into geometric configurations within circles.
Formula
Angle Formed by a Chord and a Tangent:
Angle = 0.5 * (180° – Central angle subtended by the chord)
Where:
- Angle: The angle formed between the tangent and the chord.
- Central angle subtended by the chord: The angle at the center of the circle that the chord subtends.
Angle Formed by a Secant and a Tangent:
Angle = 0.5 * (Measure of the intercepted arc)
Where:
- Angle: The angle formed between the secant and the tangent.
- Measure of the intercepted arc: The measure of the arc intercepted by the secant and the tangent.
General Terms
| Term | Description |
|---|---|
| Chord | A line segment with both endpoints on the circle |
| Tangent | A line that touches the circle at one point |
| Secant | A line that intersects the circle at two points |
| Central Angle | An angle whose vertex is at the center of the circle |
| Intercepted Arc | The portion of the circle cut off by a secant and a tangent |
Example
Let’s consider a circle with a radius of 5 units. A chord of length 8 units is drawn within the circle. Using the calculator, we can find the angle formed between this chord and a tangent drawn from one of its endpoints.
- Given: Central angle subtended by the chord = 120°
- Using the formula: Angle = 0.5 * (180° – 120°) = 30°
- Therefore, the angle formed between the chord and the tangent is 30°.
Most Common FAQs
A chord is a line segment with both endpoints on the circumference of a circle. It is the longest possible line segment that can be drawn within a circle.
To calculate the angle between a secant and a tangent, measure the intercepted arc created by the secant and the tangent. Then, apply the formula: Angle = 0.5 * (Measure of the intercepted arc).
Yes, the Angles Formed by Chords, Secants, and Tangents Calculator can be used for any circle, regardless of its size or radius.