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Common Tangents Some common tangents of two circles can be drawn.You can find that the number of them varies by the condition of the distance and radii of two circles.Using the applet of Common Tangents, try to explore this relation to the common tangents. Using the applet of Common Tangents In this applet you can explore the number of common tangents, dragging to change the radii or to move the circles.The button of@"Init"@is for replacing the figure in the initial state.If you click the button of@"Auto",@the circles are moving automatically, and then you can enjoy their performance.
Using the formula of x^2 +2gx +y^2 +2fy +c = 0 it works out that the centre of the circle is at (6.5, 3) and its radius is 2.5 units in length. Alternatively plot the points on the Cartesian plane to find the centre and radius of the circle.
Tangents stem from the origin: (0, 0) Circle equation: x^2 +y^2 -6x +4y +10 = 0 Completing the squares: (x+2)^2 +(y-3)^2 -4 -9 +10 = 0 So: (x+2)^2 +(y-3)^2 = 3 which is the radius squared Centre of circle: (-2, 3) Distance from (-2, 3) to (0, 0) = 13 which is distance squared Lengths of tangents using Pythagoras: 13-3 = 10 => square root of 10 Take note that the distance from (-2, 3) to (0, 0) is actually the hypotenuse of a right angle triangle.
Using 3.14 as Pi the area of circle is: 0
x2+y2-4x-6y-3 = 0 Using the appropriate formula it works out as:- Centre of circle: (2, 3) Radius of circle: 4.