## How to find the point on a circle when a point within it is projected out on to it?

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I need to find the coordinates of a point on a circle (point b in the picture) using the variables shown in the picture.

I know this is quite a maths related problem but i'm writing the program which this is going to be part of in python. I've tried the following code and had no luck, i've check the angle its passing though and that's correct. I've also tried the angle in radians and degrees both with no luck.

int_x = r * math.cos(angle) int_y = r * math.sin(angle)

Please ask any questions about the problem

Thank you

Given the position of `angle`

in the diagram, if you were to draw a triangle that encloses `angle`

, you'd find that `int_x`

is `opposite`

the `angle`

and `int_y`

is adjacent, which means you have your equations flipped (i.e. `int_x = r * sin.cos(angle)`

)

**Ex: Find the Point on a Circle Given an Angle and the Radius ,** Ex: Find the Point on a Circle Given an Angle and the Radius they were teaching this in Duration: 3:06
Posted: 30 Jun 2012 The technique involved is to draw a line starting at the point where the line through the circle center intersects the circle circumference (Point A in Figure 2), and to extend that line until it touches the circle at any point on its’ circumference (Figure 2, Point C).

If the circle center is known to be `(c_x, c_y)`

and the point `a`

is at `(a_x, a_y)`

. Then we simply construct a line from the center through point `a`

of length `r`

. This is simply a similar triangle. We compute the hypotenuse of the triangle to be

`h = sqrt((a_x - c_x)^2 + (a_y-c_y)^2)`

and then we know that

`(b_x, b_y) = (c_x + (a_x - c_x) * r/h, c_y + (a_y - c_y) * r/h)`

.

Then you don't need to worry about angles at all! Hope that helps.

**Check if point is within radius of another point with Shapely ,** To effectively use shapely it is important to first project your coordinates into a projected coordinate system that is appropriate to your region, for example,� What's the simplest way to find the intersection point of a straight line drawn from a circle's origin through a given point within the circle through the edge of the circle. I'm looking for the intersection point of the line and the edge of the circle. I give up! Any help is much appreciated!

I cannot comment (not enough rep), so this answer is only to indicate that in Changming's answer https://stackoverflow.com/a/59636967/12575476, it should be r/h instead of h/r (twice).

**draw projection from a point inside circle and find where it touches ,** draw projection from a point inside circle and find where it touches circle just ( x4,y4), you need to know the angle that you send out the line from that point. Points of a Circle. Points on a circle. A circle in the coordinate plane has a center at (3,1). One point on the circle is (6,-3). Name three more points on the circle. The equation of a circle is X minus H squared plus Y minus K squared is equal to R squared. This might look familiar to you because it’s derived from the distance formula.

**The Circle and the Ellipse,** A circle is defined as the set of points that are a fixed distance from a center point. The distance radius for all points. By stretching a circle in the x or y direction, an ellipse is created. Let's solve for both, and find out which is larger afterward. And thus through one in the center go Also again out of the center in three Through the four in the Circle quite free The stone-craft and all the things To investigate makes the learning easy A point which in the Circle goes Which in the Square and three angles stand Hit ye the point then have ye done And come out of Need, Fear and Danger

**Tangent lines to circles,** In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to� The ray O P → , starting at the origin O and passing through the point P , intersects the circle at the point closest to P . So, the distance between the circle and the point will be the difference of the distance of the point from the origin and the radius of the circle.

**Stereographic projection,** In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane. The projection is defined on the entire sphere, except at one point: the In practice, the projection is carried out by computer or by hand using a special kind of graph paper called a (See quotient topology.)� Find minimum number to be divided to make a number a perfect square; Find whether a given number is a power of 4 or not; Find Union and Intersection of two unsorted arrays; To find sum of two numbers without using any operator; Check whether a given point lies inside a triangle or not; Find day of the week for a given date

##### Comments

- Are the coordinates of
`O`

at`(0, 0)`

? - The question is confusing. Either
`theta`

or`a`

are unnecessary to find`b`

- Thank you very much i've spotted my error and corrected it and now the code is working a charm! Thank you.
- @FinnHunt Be careful that theta is calculated by
`atan2`

, otherwise you can get surprises when`a`

is on the Y-axis. - This answer makes most sense, as the problem description with only a picture doesn't tell whether theta is between 0 and 2 pi, nor whether it's sign changes if it would be to the left, nor whether theta would always be measured starting from the up-direction.
- Thank you very much for your answer i'm going to try it now!