Lk Is Tangent To Circle J At Point K. (2024)

FAQs

What is the equation of the tangent to a circle at a point? ›

A tangent to a circle at point P 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 = m x + c .

General equation of the tangent to a circle: 1) The tangent to a circle equation x² + y² = a² for a line y = mx +c is given by the equation y = mx ± a √[1+ m²]. Thus, the equation of the tangent can be given as xa₁+yb₁ = a², where (a1,b1) a 1 , b 1 ) are the coordinates from which the tangent is made.

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. In the circle , P T ↔ is a tangent and O P ¯ is the radius.

Tangent to a circle is the line drawn from an outside point or the point on the circumference of the circle, that touches the circle at a unique single point on its circumference. Tangent is always perpendicular to the radius of the circle. Point of tangency refers to the point at which the tangent meets the circle.

The equation for the line tangent to a curve at a point (x1,y1) ( x 1 , y 1 ) is given by y−y1x−x1=m1 y − y 1 x − x 1 = m 1 . Here x1=1 x 1 = 1 , y1=−2 y 1 = − 2 and m1=16 m 1 = 16 , so the equation for the tangent line at this point is: y−(−2)x−1=16.

The tangent at any point of a circle is perpendicular to the radius through the point of contact. Proof: Consider a circle with centre “O” and XY is the tangent to a circle with the point of contact “P”. To prove: OP is perpendicular to XY.

Let us consider a right-angled triangle with one of its acute angles to be x. Then the tangent formula is, tan x = (opposite side) / (adjacent side), where "opposite side" is the side opposite to the angle x, and "adjacent side" is the side that is adjacent to the angle x.

A tangent is a straight line that touches the circumference of a circle at only one point. The angle between a tangent and the radius is 90°. • Two tangents on a circle that meet at a point outside the circle are equal in length.

This theorem states that if from one external point, two tangents are drawn to a circle then they have equal tangent segments. Tangent segment means line joining to the external point and the point of tangency. Consider the following diagram: Here, AC=BC.

Theorem 2: Two Tangents Theorem

The lengths of two tangents from a common external point to a circle are equal. The two tangents will subtend equal angles at the center. The line that connects the exterior point to the center will divide the angle between the tangents into two equal angles.

What is an equation of a circle? ›

Explanation: The general equation of a circle is (x – h)² + (y – k)² = r², where (h, k) represents the location of the circle's center, and r represents the length of its radius.

Remember, the point-slope formula y−y1=m(x−x1) is the best way to compute the equation of the tangent line, for reasons that will become apparent later, so practice with that form of the line (even if you have a preferred other method, such as plugging in a point to the slope-intercept form y=mx+b.

That is, the square of the length of the tangent to the circle is equal to the square of the distance between the centre and the point P (from which the tangent is drawn), minus the square of the radius.

Parametric Form:

The point P(x₁, y₁) as discussed in the point form, in parametric coordinates becomes x₁ = a cos θ and y₁ = a sin θ. The equation of the tangent in this case becomes x cos θ + y sin θ = a.