# Tagged Questions

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### Simple algebraic question mixed up

I know it is very simple but do not know why I am mixed up in it $(.5)(r^2)\cfrac{20-2r}r$ how is this equal to $10r-r^2$ Sorry if it is too easy, thanks for the help.
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### Finding the release angle for projectile

Hello. I would like to create an game application for android platform that is similar like projectiles. I called it snowball machine. As you know regular projectiles has to hit the ...
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### Sine defined for a triangle inscribed in a circle with a diameter of one

Let a circle be drawn with a diameter of one (and thus a radius of one half). Then let a triangle with vertices A, B, and C be inscribed in the circle (i.e. points A, B, and C are arbitrary points on ...
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### Arc Length from chord and tangent angle

This is for a rubberband-powered car competition. In the diagram above, I will be given the length from points A to B, as well as angle a. The car will need to go from A to B, positioned at a to ...
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### Radius of circle by knowing a cross section.

I have a curve on an ellipse where I know the length of a cross section and need to find out it's radius (vertically and horizontally) and calculate the angle of the curve. In the following diagram ...
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### How do you prove arc length is greater than chord length?

Graphically, it's obvious that given two different points $a$ and $b$ on a circle of radius $r$, the linear distance (chord length) from $a$ to $b$ is less than the arc length from $a$ to $b$. How do ...
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### Radian and the length of a chord of a circle

Question In a circle of radius $r$, an arc of it is $2S$ long. Find the length of the chord corresponding to that arc (AB in the diagram below) . Details I got this question in a math test. And ...
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### Find a circle's radius with three known tangent lines

I need to find the equation for a circle (mainly its radius) which is tangent to the following three lines: $y = 0$ $y = \tan(70)x$ $y = -1.428148x + 0.790201$ For the last tangent line equation, ...
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### Find radius of a circle which is tangent to three known lines

I need to find the equation for a circle which is tangent to the following three lines: y=0 x=0 y=-x+0.338334 For the last tangent line equation, I know that it is tangent at the point (0.169167, ...
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### How do I proof that $\angle ABP =\angle AP'B$ and that $P$, $Q$, $Q'$ and $P'$ are on 1 circle?

Given is a circle with center $M$ and a diameter $AB$. $k$ is the tangent to the circle at point $B$. On the circle there are two points called $P$ and $Q$, such that $P$ and $Q$ are both on the same ...
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### Euclidean geometry: Circle incribed in a circle

Circle $c_2$ - with center $N$ - is inside circle $c_1$ and is tangent to circle $c_1$ - with center $M$ - in $P$. The line $l$ intersects $c_1$ at points $A$ and $D$ and $c_2$ at points $B$ and $C$. ...
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### Circle equation with sine without parametric equation

I had to integrate an area delimited by a quarter of a circle, something like this: http://www.wolframalpha.com/input/?i=integrate+10+-+sqrt%2864+-+x%5E2%29+dx+from+0+to+5 Which comes from the ...
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### how to find sin13° cos13° tan13° cot13° with trigonometric circle.

I have problem finding sin(13°) cos(13°) tan(13°) cot(13°)with trigonometric circle. I have to draw the circle with a triangle on it but I can't get the right thing.
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### Derivation of the length of an arc formula

My textbook says that the radian measure of an angle is the ratio: $\theta = \frac{s}{r}$ Where s is a portion of the entire circumference, and r is the radius. So essentially the arc length is thus: ...
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### Contract expression of circle segment area contingent on height

I want to determine a function for the area of the segment's height. I have made it this far, but I would like to contract the equation further - sadly, I do not know how to do this while still ...
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### Finding the coordinates of the top and bottom circles of a moving and rotating cylinder in 3D

I have a cylinder that is moving and rotating in a 3D space. I need to calculate the coordinates of the center of the cylinder's top and bottom circles. Here's the information I have : I have at the ...
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### Problems with Circles and Lines on a Cartesian Plane

(a) Find the equations of the two circles each of which touches both coordinate axes and passes through the point $(9,2)$. (b) Find the coordinates of the second point of intersection of the two ...
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### How to find the equation of a line tangent a circle and a given point outside of the circle

I am given the equation of a circle: $(x + 2)^2 + (y + 7)^2 = 25$. The radius is $5$. Center of the circle: $(-2, -7)$. Two lines tangent to this circle pass through point $(4, -3)$, which is outside ...
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### Simple circle geometry/ similarity question

How would you prove that a=b? Would i be possible to solve this using similarity or trigonometry? Thankyou in advance for any help. Any theorems or links would be appreciated
284 views

### If inside a big circle , exactly n $(n \geq 3)$ small circles, each of radius r,can be drawn in such a way that each small circle touches t…

Problem : If inside a big circle , exactly n $(n \geq 3)$ small circles, each of radius r,can be drawn in such a way that each small circle touches the big circle and also touches its adjacent small ...
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### Let P be a moving point such that if $PA$ and $PB$ are two tangents drawn from $P$ to the circle $x^2+y^2=1 ($ A ,B being the points of contact) ,…

Problem : Let $P$ be a moving point such that if $PA$ and $PB$ are two tangents drawn from $P$ to the circle $x^2+y^2=1$ ( $A$, $B$ being the points of contact) , then $\angle AOB = 60^{\circ}$, ...
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### Equation of a Circle from parametric functions of sin and cos

Given: x = 2 cos (t/2) y = 2 sin (t/2) How do we find the equation of the circle? I know that x^2 + y^2 = 1, where x = cos(t) y = sin(t) so x^2 = (2 cos (t/2))^2 y^2 = (2 sin (t/2))^2 How do ...
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### What am I doing wrong in this trigonometry/rate simulation problem?

I'm refreshing on some trig and cannot figure out how to solve this non-realistic word problem simulating a person walking in a circle. A person is located at the point (8,0) at time, t = 0, and ...
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### Sectors of a Circle

I am programatically drawing sectors of a circle with radius 55 on a cartesian plane which runs from -55 to 55 on the x and y axes. I would like the first sector to be drawn at 0,55. I know I can ...
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### Proof Error? A line-segment of a circle is a metric.

In O'searcoid, Metric Spaces, he provides the following example of a metric space: Suppose C is a circle and, for each $a,b ∈ C$, define $d(a,b)$ to be the distance along the line segment from $a$ ...
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### Intersection of a point and absolute value function contained within a circle

I'm attempting some crazy ideas while programming a game and ran into the following math problem that has been bugging me for a few days: Given a unit circle and a random point $P$ within the circle, ...
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### Is there a continuous version of $tan^{-1}(\frac{y}{x})$ for the entire unit circle?

The fact that $tan^{-1}(\frac{y}{x})$ only "works" for the upper-right quadrant makes some calculations (for a physics simulator) impossible. I of course use $atan2(y,x)$ in the code, that's not what ...
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### $\pi$ is just a number, or also the circumference of a sub-unit circle?

A unit circle defined in the Cartesian plane has a radius of $1$ and a diameter of $2$. So making a full round is $2 \pi$. Now, $\pi$ is the ratio of the circumference over the diameter, so if I have ...
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### Circular motion trig

We have $x_P = -2 + 4 \cos (-\pi t)$ and $y_P = 1 + 4 \sin ( - \pi t)$ with $t$ in seconds. We have to find the coordinates of the intersection with the y-axis. So I use trig and I eventually end up ...
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### How to find a point on the tangent line whos length is 1?

im trying to figure out a formula to find the point(x,y) on a tangent line whos length is between 0 and 1 while it rotates around the unit circle uniformly, so the point would either be right on the ...
2k views

### Calculating circle radius from two points and arc length

For a simulation I want to convert between different kind of set point profiles with one being set points based on steering angles and one being based on circle radius. I have 2 way points the ...
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### Calculate points(x, y) within an arc

I am trying to draw lines from the center of a circle to points (x, y) in the circumference. To calculate this the angle is used. I need to render points in between two angles. E.g. Angle 0 to angle ...
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### Calculating circle properties.

How can I incrementally calculate the angle from angle 0 and the point (x, y) in a circumference path if I have the center of the circle coordinates and the radius of the circle. I have 127 segments ...
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### Calculating mean velocity of an orbiting body as it moves towards a point.

I'm making a game, in the game planets orbit a central point in circular orbits, they move directly towards their targets and the vector is simply added to their orbital path. Whilst not realistic it ...
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Alright, I was doing a question in a book, and it said: $\displaystyle \cos(2x - \frac{\pi}{6}) = \frac{\sqrt{3}}{2}$ I proceeded and got: $\displaystyle 2x - \frac{\pi}{6} = \frac{\sqrt{3}}{2}.$ I ...
284 views

### Finding side and angle of isosceles triangle inside two circles

I'm having a problem that I'm not sure how to solve (or if it's even possible). It's not homework, just something I'm struggling with for a project. :) Basically, there are two circles, represented ...
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### How do you calculate the velocity of the pencil?

I'm drawing a quarter circle with a pencil on a sheet of graph paper. The radius is 10cm. At a given moment in time the velocity at which I am moving the pencil is 5cm/s (centimeters per second). I ...
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### Given one endpoint on an arc of a circle and the radius and arc angle, how to calculate the other endpoint of the arc?

I have a circle with an arc beginning at point $(x,y)$. The radius is $r$, the arc angle(w/ respect to center) is $\theta$. How do I calculate the end point of the arc $(a,b)$ ? I know that the ...
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### How does one calculate the product of $\tan 1^{\circ} … \tan 45^{\circ}?$

I have seen a question asked on yahoo asking to find the value of $\tan 1^{\circ} \cdot \tan 2^{\circ} \cdot \dots \cdot \tan 45^{\circ}$ (in degrees) I have seen various results concerning ...
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### How to find an end point of an arc given another end point, radius, and arc direction?

Given an arbitrary arc, where you know the following values: end point (x1,y1), radius (r) and arc direction (e.g. clockwise or counterclockwise from start to end), how can I calculate the other ...