How Do I Find the Equation of the Tangent From Any Point Outside the Circle to That Circle?

Let M(p, q) be the point outside the circle.Let C(x1, y1) be the center of the circle and r it's radius. Let T(x, y) be the point of tangency. CT will be normal to TM. Eqn of TM : y- q = m (x - p). Slope of CT = -1/m. Eqn of CT: my x = my1 x1. Solve for intersection of CT and TM which is T(x, y) in terms of p, q and m.

1. Generating visually pleasing circle packs

The idea is toInstead of working with graphics primitives and the position of circles and their radii I work with the image matrix directly.Code:Adjustable parameters are the paddings, the size of the circles and for how long it continues to try to pack the shape.With the color scheme BlueGreenYellow and shape = DiskMatrix we getWith the color scheme DeepSeaColors andwe getFinally, this is a circle packed map of Sweden using the color scheme DarkTerrain:The careful observer will note that the smallest objects are not actually round. Do not worry about this, it's because the smallest object is just one pixel and you can not make a circle out of that. It saved me time to generate the graphics like this, it can easily be fixed by making a larger image and setting the smallest circle to a radius of say three or five, then shrinking the image to whatever size one wants

2. 3D coordinates of circle center given three point on the circle.

I think using a projection into 2D might be the easiest way to actually calculate. If the points are $A, B, C$ then find $$beginalign mathbfu_1 & = B-A mathbfw_1 &= (C-A) times mathbfu_1 mathbfu & = mathbfu_1 / | mathbfu_1 | mathbfw & = mathbfw_1 / | mathbfw_1 | mathbfv & = mathbfw times mathbfu endalign$$This gives three orthogonal unit vectors with $mathbfu$ and $mathbfv$ spanning the plane. Get 2D coordinated by taking the dot products of $(B-A)$ and $(C-A)$ with $mathbfu$ and $mathbfv$. Let $$beginalign b & = (b_x,0) = ( (B-A) cdot mathbfu , 0 ) c &= (c_x,c_y) = ( (C-A) cdot mathbfu, (C-A)cdot mathbfv ) endalign$$We know the center must lie on the line $x= b_x/2$. Let this point be $(b_x/2,h)$. The distance from c must be the same as the distance from the origin $$(c_x-b_x/2)^2 (c_y - h)^2 = (b_x/2)^2 h^2$$ So $$h = frac(c_x-b_x/2)^2 c_y^2 - (b_x/2)^2 2 c_y $$The actual center can then be recovered by taking $A (b_x/2)mathbfu h mathbfv$.This is a nice explicit calculation.

3. How to get a circle over A

Do not redefine

as this is the 'ring' used over ''

4. Determining the Diameter of a Circle

Yes is valid. I do not know where is your confusion but notice that $x^2y^2geq 0$. Therefore $sqrtx^2y^2$ is always well defined in the sense that you get a real number as a result, and of course is legal two divide by two. So the expression is mathematically valid and you are able to calculate it for any point $(x,y)$ of the space. The reasoning of deduction of the formula is also flawless.

5. Open sets on a circle

An open set is technically a closed set, taken out the boundary. In your case, for simplicity let us assume $1$ be the circumference of the circle. Then $(0,1)$, the set of all points from $0$ to $1$ excluded the two points at the ending is one such open set. Hope that helps :)

6. circle becomes an oval after saving

I just ran into the same issue editing a layer in WGS 1984. I created a new shapefile without a defined projection and the distortion did not occur after I saved the edits. Looks like Zbynek was correct, it is a projection issue. Try projecting the layer into what your mxd is projected in and maybe redrawing the circle

7. Is there some sort of device that let's you cut a near perfect circle/half circle?

For large circles, there are arrangements that rotate a sheet of metal under a laser or cutting torch

8. Intercept of sine with circle

We find maximum and minimum of functions:For sinusoide:$y=4 sin (0.5 x -1) implies y' = 0.5 cos (0.5 x -1)= 0 implies x/2 -1= pi/2 implies x_s=pi 2$ and $y_s =4$ is maximum point. Also sinusoide cross x axis at points $2, 0$ and $(x = 2pi 1 7. 28, 0) $ For circle maximum is $(x_c, y_c)= (4, 5)$ and minimum is $(x_c, y_c)=(4, 1)$We can see that $2

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Wedding Dress of Birgitte Van Deurs
Wedding dress of Birgitte van DeursThe wedding dress of Birgitte van Deurs was worn at her wedding to Prince Richard of Gloucester on 8 July 1972 at St Andrew's Church, Barnwell, Northamptonshire. The dress was designed by Norman Hartnell, who first collaborated with the British royal family for the wedding dress of the groom's mother, Princess Alice, Duchess of Gloucester. The dress was constructed of Swiss organdie, with a high collar, a simple skirt, long sleeves and a small train. Instead of wearing a tiara, the bride secured her white tulle veil with a grouping of stephanotis flowers. The dress was regarded by some as one of Hartnell's more modern creations for the time, incorporating some stylistic features of 1970s fashion.— — — — — —Wedding dress of Princess AliceThe wedding dress of Princess Alice of the United Kingdom was worn during a period of court mourning for the death of her father. Princess Alice was the second daughter of Queen Victoria and Prince Albert. On 1 July 1862, in the dining room of Osborne House on the Isle of Wight, she married Prince Louis of Hesse. Seven months had passed since the death of the Prince Consort and the Royal Family was still in deep mourning. The venue was chosen so that the Queen would be able to avoid inviting the usual guests of state. From "The Royal Wedding Dresses" by Nigel Arch and Joanna Marschner (p.58): "She wore a 'half-high dress with a deep flounce of Honiton lace, a veil of the same and a wreath of orange blossom and myrtle'." It was a simple style and not embellished with a court train. Queen Victoria later confided to her daughter, the Princess Royal (Vicky), that the wedding of 'poor Alice' had been "more like a funeral."— — — — — —Wedding dress of Princess Helena of Waldeck and PyrmontThe wedding dress of Princess Helena of Waldeck and Pyrmont was worn by the bride at her wedding to Prince Leopold, Duke of Albany, on 27 April 1882 in St. George's Chapel, Windsor Castle. Prince Leopold was the youngest son of Queen Victoria and Prince Albert. Princess Helena was the daughter of George Victor, Prince of Waldeck and Pyrmont and his wife Princess Helena of Nassau. The dress was made in Paris and was presented by her sister, Queen consort Emma of the Netherlands. The gown was made of white satin, decorated with traditional orange blossom and myrtle and trimmed with fleur-de-lis, with the edge topped with point d'Alenon and white satin. The long tulle veil was held in place by a diamond head dress and a wreath of orange blossoms and myrtle. The shoulders were bare and the short drop sleeves adorned with the Royal Family Order of the Royal Order of Victoria and Albert and the Companion of the Order of the Crown of India pinned to the left. The bosom was swathed in tulle and ruched laces with a small bouquet of flowers. The fashionably cut bodice ended in a sharp V-shape that accentuated the bride's tall and slender figure. Helena received large diamond sprays from the King and Queen of the Netherlands, which she wore as a tiara and brooch on her wedding day. From her parents, she received a diamond necklace and sun rays that she also wore as brooches. Prince Leopold gave his bride a diamond necklace, a large diamond star, a ruby bracelet, a ruby and diamond bracelet, sapphire and diamond earrings, Spanish lace, and a fan, which can also be seen in her wedding photos.— — — — — —Getting married and have so much to do! Lose weight, quit smokng, plan the wedding, finish school! HELP!?I was the same size when I got married, and 5 feet tall, and wore a size 18 wedding dress. There is a special full length bra that you wear under the wedding dress that will make you look like you did a million sit ups, raise your bust to look like you were perfectly proportioned, and nobody will be the wiser. You will not look like a Fat Cow— — — — — —What type of dress is this ?16 Trend colors in spring-summer 2019 Prom Party Dresses Triumph at next year's weddings with the trendiest colors. Experts have already sighted the shades that will cause rage at all parties. Choose your guest look or help your ladies and set a trend with these tones! At weddings, each color is unrepeatable: the white of the wedding dress, the shades on the ribbons of the little ties, the prints of the groom's tie, and which one is best for the guests to dress? If for this spring-summer you have already received several wedding invitations, be the most glamorous guest with these colors. And if you are looking for party dresses for your ladies choir, let yourself be carried away by the color shades of spring-summer 2019.
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