Tangent Lines Homework PDF and Answer Key (Unit 10: Circles) (Geometry) as PDF - Knowunity (2024)

FAQs

What is tangent answers? ›

In Geometry, the tangent is defined as a line touching circles or an ellipse at only one point. Suppose a line touches the curve at P, then the point “P” is called the point of tangency. In other words, it is defined as the line which represents the slope of a curve at that point.

A line that touches the circle at a single point is known as a tangent to a circle. The point where tangent meets the circle is called point of tangency. The tangent is perpendicular to the radius of the circle, with which it intersects.

We can draw only one tangent to a circle through a point that lies on the circle. A tangent cannot be drawn from a point lying inside the circle.

A tangent of a circle is a straight line that touches the circumference of the circle at only one point. The angle between a tangent and radius is 90 90 90 90 degrees. Tangents which meet at the same point are equal in length.

A tangent is a line that touches the curve or a circle at a point. The point at which the tangent line and the curve meets is called the point of tangency.

In any right triangle, the tangent of an angle is the length of the opposite side (O) divided by the length of the adjacent side (A). In a formula, it is written simply as 'tan'.

The equation of the tangent line can be found using the formula y – y₁ = m (x – x₁), where m is the slope and (x₁, y₁) is the coordinate points of the line.

The radius of a circle is perpendicular to the tangent line through its endpoint on the circle's circumference. Conversely, the perpendicular to a radius through the same endpoint is a tangent line. The resulting geometrical figure of circle and tangent line has a reflection symmetry about the axis of the radius.

No tangent line can be drawn through a point within a circle, since any such line must be a secant line. However, two tangent lines can be drawn to a circle from a point P outside of the circle.

The Two-Tangent Theorem states that if two tangent segments are drawn to one circle from the same external point, then they are congruent.

When a tangent touches a circle? ›

The point where the tangent touches the circle is called “Point of contact”.

The gradient or slope of a line (not parallel to the axis of y) is the trigonometrical tangent of the angle which the line makes with the positive direction of the x-axis. Thus, if a line makes an angle θ with the positive direction of the x-axis, then its slope will be tan θ.

A tangent to a circle is a straight line which touches the circle at only one point. This point is called the point of tangency. The tangent to a circle is perpendicular to the radius at the point of tangency.

Final answer: The term 'tangent' originates from Latin and in mathematics refers to a line that touches a curve at a single point, while in common language, it means veering off-topic.

: to start talking about something that is only slightly or indirectly related to the original subject.

The tangent function can be expressed as the ratio of the sine function and cosine function. It is the ratio of the opposite side and the adjacent side of the angle in consideration in a right-angled triangle.