Table of Contents
How do you determine whether a line is tangent to a circle?
The easiest way is to solve the system between the equation of the circle and the equation of the line. The equation that solves that system is quadratic. If the Δ of that equation is zero, the line is tangent, if it is positive the line is secant, if it is negative the line is external.
How do you determine if a line is secant to a circle?
A secant is a line that intersects a circle in exactly two points. When a tangent and a secant, two secants, or two tangents intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.
How do you tell if a line is secant or tangent?
The secant line is the red line to the right that passes through two points on the curve. The tangent line is the green line that just grazes the curve at a point.
How do you solve a secant in a circle?
Two Secants Intersecting Formula: If two secant segments are drawn from a point outisde a circle, the product of the lengths (C + D) of one secant segment and its exteranal segment (D) equals the product of the lengths (A + B) of the other secant segment and its external segment (B).
What is secant and tangent of a circle?
Tangents and secants are the lines that cut the circle and extend in both directions infinitely. The main difference between them is that a secant cuts the circle at two points, whereas, a tangent cuts the circle at one point. The tangent is perpendicular to the radius at the point of the tangency.
How do you write the equation of a circle?
Correct answer: The formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle.
What is the formula for tangent secant of a circle?
The formula for tangent-secant states that: PS 2 = PQ.PR The tangent line never crosses the circle, it just touches the circle. At the point of tangency, it is perpendicular to the radius. A chord and tangent form an angle and this angle is same as that of tangent inscribed on the opposite side of the chord.
How do you find the secant of a straight line?
A straight line which cuts curve into two or more parts is known as a secant. So, here secant is PR is drawn and at Q, R intersects the circle as shown in the upper diagram. The formula for tangent-secant states that: PS 2 = PQ.PR The tangent line never crosses the circle, it just touches the circle.
What is the tangent to a circle at point P?
A tangent to a circle at point P with coordinates \\ ( (x, y)\\) is a straight line that touches the circle at P. The tangent is perpendicular to the radius which joins the centre of the circle to the point P. As the tangent is a straight line, the equation of the tangent will be of the form \\ (y = mx + c\\).
What is the equation of a circle without sketching?
The equation of a circle is ( x 2 5) 2 1 (y 2 1) 2 5 9. Without sketching the circle, tell whether the point is on the circle, inside the circle, or outside the circle. a. Substitute the coordinates of the point into the equation.