In the xy-coordinate system, a circle has center C with coordinates (6, 2.5). This circle has exactly one point in common with the x-axis. If the point (3.5, t) is also a point on the circle, what is the value of t? The formula of a circle is (x - a)2 + (y - b)2 = r2 Where r is the radius, and the centre is at (a,b). This is all down to Pythagoras' theorum - see if you can see why. Anyway, the question gives us the values of a and b as 6 and 2.5. Since the x axis is tangential to the circle, we can also deduce that r = b. This completes the formula: (x - 6)2 + (y - 2.5)2 = 2.52 = 6.25 To answer the question, substitute in x = 3.5 and y = t so that we can find t. (3.5 - 6)2 + (t - 2.5)2 = 6.25 (-2.5)2 + (t - 2.5)2 = 6.25 6.25 + (t - 2.5)2 = 6.25 (t - 2.5)2 = 0 t - 2.5 = 0 t = 2.5 We reached the answer by a purely algebraic method. A sketch graph and some clear reasoning would have served just as well: clearly (3.5,t) is level with the centre of the circle, because its displacement in the x direction is equal to the radius r.
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.
The radius and the tangent are perpendicular at the point on the circle where they meet.
Equation of circle: x^2 +8x +y^2 -9 = 0 Completing the square: (x+4)^2 +y^2 = 25 Radius of circle: 5 Center of circle: (-4, 0) Distance from (9, 0) to (-4, 0) is 13 which is the hypotenuse of a right angle triangle Using Pythagoras' theorem: 13^2 -5^2 = 144 and its square root is 12 Therefore length of tangent line is: 12 units Note that a tangent line always meets the radius of a circle at right angles.
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.
It simply means where the horizon (where earth meets sky) sits in the frame. It is generally boring to keep it in the center. It stops the eyes. Try framing so there is a lot of sky, a little sky with the camera level.
Continue or follow the inner or outer trajectory of the radius arc line in either, or both, directions until it meets itself. The i will have a center point which is at a fixed distance from the arc, equal to one half of the radius of the finished circle, and which will thereby prove the circle.
A diameter - provided it meets the boundary of the circle or sphere on opposite sides.
The tangent line. A secant line hits the circle in two places and forms a cord, but the tangent line only hits the circle in one point and is always perpendicular to the radius of the circle which exists at that point.
A chord is a straight line drawn through a circle which divides the circle into two parts. The line can be drawn anywhere in the circle EXCEPT the center where it becomes the diameter.
It is: (x-3)2+(y+5)2 = 13
From any point on the circumference of the circle, draw a line going through the center and continuing until it meets the circumference again. Measure this line. This is the diameter of the circle. If the centre is not marked, simply take a ruler and find the widest measure you can make across the circle. See the related link below, The Parts of the Circle.
The tangent of a circle always meets the radius of a circle at right angles.
a tangent to the circle
Equation of circle: x^2 +y^2 -2x -6y +5 = 0 Completing the squares: (x -1)^2 +(y -3)^2 = 5 which is radius squared Center of circle: (1, 3) Tangent line is at right angles to the radius at (3, 4) and meets the x axis at (5, 0) Distance from point (5, 0) to center of circle (1, 3) = 5 units using distance formula
A point and most of the time meets, a polygon is a circle thing that meets at some point!
they will love them to
tangant of circle intercepts it only on one point. In real the point where tangent meets the circle and intercepts it are same