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A tangent of a circle in geometry is defined as a straight line that touches the circle at only one point. The tangent formula is the tangent to circle equation which is y = mx ± a √[1+ m2], if the tangent is represented in the slope form and the tangent to the circle equation is x\(a_1\)+y\(b_1\)= a 2 when tangent is given in the two-point ...
To find the equation of a tangent to a circle: Find the gradient from the centre of the circle to the tangent point. Calculate the negative reciprocal of this gradient to find ‘m’.
- Definition
- General Equation
- Condition of Tangency
- Tangent Properties
- Tangent Formula
- Tangent Theorems
- Solved Example
Tangent to a circle is the line that touches the circle at only one point. There can be only one tangent at a point to circle. Point of tangency is the point at which tangent meets the circle. Now, let’s prove tangent and radius of the circleare perpendicular to each other at the point of contact. Consider a circle in the above figure whose centre ...
Here, the list of the tangent to the circle equation is given below: 1. 1.1. The tangent to a circle equation x2+ y2=a2 at (x1, y1) isxx1+yy1= a2 1.2. The tangent to a circle equation x2+ y2+2gx+2fy+c =0 at (x1, y1) is xx1+yy1+g(x+x1)+f(y +y1)+c =0 1.3. The tangent to a circle equation x2+ y2=a2 at (a cos θ, a sin θ ) isx cos θ+y sin θ= a 1.4. The ...
The tangent is considered only when it touches a curve at a single point or else it is said to be simply a line. Thus, based on the point of tangency and where it lies with respect to the circle, we can define the conditions for tangent as: 1. When point lies inside the circle 2. When point lies on the circle 3. When point lies outside the circle
The tangent always touches the circle at a single point.It is perpendicular to the radius of the circle at the point of tangencyIt never intersects the circle at two points.The length of tangents from an external point to a circle are equal.Suppose a point P lies outside the circle. From that point P, we can draw two tangents to the circle meeting at point A and B. Now let a secant is drawn from P to intersect the circle at Q and R. PS is the tangent line from point P to S. Now, the formula for tangent and secant of the circle could be given as: PR/PS = PS/PQ PS2=PQ.PR
Theorem 1:The tangent to the circle is perpendicular to the radius of the circle at the point of contact. Theorem 2:If two tangents are drawn from an external point of the circle, then they are of equal lengths
Example:AB is a tangent to a circle with centre O at point A of radius 6 cm. It meets the line OB such that OB = 10 cm. What is the length of AB? We know that AB is tangent to the circle at A. Since tangent AB is perpendicular to the radius OA, ΔOAB is a right-angled triangle and OB is the hypotenuse of ΔOAB. By using Pythagoras theorem, To know mo...
The equation of the tangent line of the circle is given by: (x - x₁)(x₁ - a) + (y - y₁)(y₁ - b) = 0.
A tangent of a circle is a straight line that touches the circle at only one point. Let’s explore the definition, properties, theorems, and examples in detail.
Aug 3, 2023 · How to Find the Tangent of a Circle. The formula to calculate the tangent of a circle is derived below: Suppose a point ‘T’ lies outside the circle. From that point, we will draw two tangents to the circle. In the given figure, if ‘RT’ is the secant and ‘QT’ is the tangent of the circle, then the relation between the secant and the ...
Jun 1, 2024 · With our calculator, you can input any point that lies on a circle's circumference, and it will instantly output the equation for a line tangent to the circle at that point. Or, you can manually find the expression for the tangent line by replacing the values for x x x and y y y in the following equation:
