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To find the area of triangle OAP, where O is the origin (0,0) and A is the point (2, 6), we first need to determine the coordinates of point P where the tangent line intersects the x-axis. The slope of the radius OA at point A is -13/5, so the slope of line L, being tangent, is the negative reciprocal, 5/13. The equation of line L can be found using point A, and we can determine the x-intercept to find point P. Finally, the area of triangle OAP can be calculated using the formula: Area = 0.5 * base * height, with the base being the distance from O to P and the height being the y-coordinate of point A.
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A triangle is inscribed in the circle x squared plus y squared equals 25 Find the dimensions of the triangle which will have the maximum area?
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Tangent of a circle is what?
A tangent of a circle is a straight line that touches the circle at only one point.
What is it called when the circle is inside the triangle Geometry?
When a circle is inscribed within a triangle, it is called the "incircle." The center of the incircle is known as the "incenter," which is the point where the angle bisectors of the triangle intersect. The incircle is tangent to each side of the triangle, touching them at precisely one point.
What are the possible value of k when the line y equals x plus k is a tangent to the circle x squared plus y squared equals 25?
They are +/- 5*sqrt(2)
Where is the tangent secant angle on a circle?
The tangent secant angle is the angle between the tangent to a circle and the secant, when the latter is extended.
A polygon in which each side is tangent to the circle?
A square or an equilateral triangle for example when a circle is inscribed within it.
A triangle is inscribed in the circle x squared plus y squared equals 25 Find the dimensions of the triangle which will have the maximum area?
There is a ninja behind you
Does a trigonometry tangent relate to a circle's tangent?
A circle's tangent is exactly the same as a triangle's tangent. If you look at a circle, you can make the radius the hypotenuse. Then make a vertical line from the point, and a horizontal line from the center. If you look, you have a triangle made inside the circle. This is why angles can be measured in radians, a unit that is derived from the circumference of a circle.-------------------------------------------------------------------------------------------By doing a little calculus, we find that the slope of the equation of a circle-the slope of the tangent line-is given by the tangent of an angle.AnswerEverything written above is correct, but doesn't have anything to do with tangents (in the circle sense of the word). Suppose you're given an angle theta. Draw a circle together with two radii, one horizontal and the other at an angle theta from the first one. (So far, this is the same as above.) Now draw the tangent to the circle at X, the point where the non-horizontal radius meets the circumference. Let Y be the point where this tangent meets the horizontal line through the centre. Then, assuming the radius is 1, tan(theta) is the distance XY, which is the length of part of the tangent.
Tangent of a circle is what?
A tangent of a circle is a straight line that touches the circle at only one point.
What is the Tangent Line to Circle Theorem?
The Tangent Line to Circle Theorem states that a line is tangent to a circle if and only if it's perpendicular to the circle's radius.
What is it called when the circle is inside the triangle Geometry?
When a circle is inscribed within a triangle, it is called the "incircle." The center of the incircle is known as the "incenter," which is the point where the angle bisectors of the triangle intersect. The incircle is tangent to each side of the triangle, touching them at precisely one point.
What is the tangent equation that touches the circle of x squared plus y squared -8x -y plus 5 equals 0 at the point of 1 2 on the Cartesian plane showing work?
Equation of circle: x^2 +y^2 -8x -y +5 = 0Completing the squares: (x-4)^2 +(y-0.5)^2 = 11.25Centre of circle: (4, 0.5)Slope of radius: -1/2Slope of tangent: 2Equation of tangent: y-2 = 2(x-1) => y = 2xNote that the above proves the tangent of a circle is always at right angles to its radius
What is the equation of the tangent line that touches the circle x squared plus y squared -8x -16y -209 equals 0 at a coordinate of 21 and 8?
Circle equation: x^2 +y^2 -8x -16y -209 = 0 Completing the squares: (x-4)^2 +(y-8)^2 = 289 Centre of circle: (4, 8) Radius of circle 17 Slope of radius: 0 Perpendicular tangent slope: 0 Tangent point of contact: (21, 8) Tangent equation: x = 21 passing through (21, 0)
What are the possible value of k when the line y equals x plus k is a tangent to the circle x squared plus y squared equals 25?
They are +/- 5*sqrt(2)
What is the length of the tangent line from the point 0 0 to a point where it touches the circle x2 plus y2 plus 4x -6y plus 10 equals 0 on the Cartesian plane?
Equation of the circle: x^2 +y^2 +4x -6y +10 = 0 Completing the squares: (x+2)^2 +(y-3)^2 = 3 Radius of the circle: square root of 3 Center of circle: (-2, 3) Distance from (0, 0) to (-2, 5) = sq rt of 13 which is the hypotenuse of right triangle. Using Pythagoras' theorem : distance squared - radius squared = 10 Therefore length of tangent line is the square root of 10 Note that the tangent of a circle meets its radius at right angles.
A line that intersects a circle at exactly one point?
Such a line is called a tangent line or a tangent to the circle. [Tangent is Latin for touching-- a tangent line touches the circle at just one point. ]
Where is the tangent secant angle on a circle?
The tangent secant angle is the angle between the tangent to a circle and the secant, when the latter is extended.
