1. T


    Find the equation of a circle with centre on the y-axis, which cuts orthogonally each of the circles x2+y2+6x+2y-9=0 and x2+y2-2x-2y+1=0. (x+3)2+(y+1)2=10, (x-1)2+(y-1)2=1 I tried to use ratio to solve it. Like 32+(y-1)2 : 1+(y-1)2 = 3:2 y2-2y+10=3y2-6y+6 y2-2y-2=0 y=1+sqrt3 hence the equation...
  2. S

    Another tough Geometry Question ( Pythagoras and Circles and Tangents)

    Hi guys, another tough problem thats giving me some trouble. I thought i might look to the geniuses on this forum for help. Anyway, i am attaching a picture, basically i have to find the radius of the circle using phythagoras. The smaller circle has a radius of 1cm and the angle between the...
  3. SheekhKebab


    Through any given set four points P,Q,R,S how many circles can be drawn ? How can we solve this using combinatoric analysis ?
  4. D

    Help needed calculating the area of a rectangle with 2 semi circles on either side

    I start University in 3 months and im going over past papers for Mathematics. I have had a good deal of success with all questions bar one. As i have finished up college i have no lecturers to ask how you would approach this and tbh its annoying me. I have spent 2 days and i feel i have hit a...
  5. J

    Distance between center of two circles

    I have to find O1O2 but I've no idea how.. Any advices ? Thank you!
  6. M

    halp solving trig formula using unit circles

    Hi, I'm working on some practice questions using unit circles in advance of a chapter quiz tomorrow and am stuck on one question that I must have a mental block about. The question is as follows: Solve the equation on the interval theta is greater than or equal to zero and less than pi...
  7. K

    Points on circles collinear

    Last one... Diagonals of quadrilateral $ABCD$ intersect in point $S$. Circle $k_1$ is circumscribed of triangle $ABS$. $k_1$ intersects line $BC$ in point $M$. Circle $k_2$ is circumscribed of triangle $ADS$ and it intersects line $CD$ in point $N$. Prove that points $S, M$ and $N$ are collinear.
  8. C

    How to plot circles in MathGV

    I cannot plot a circle because it considers 'y' as an invalid character when it try to enter 'x^2 + y^2 = 1 How then do I plot circles, I cannot find it in the help library
  9. R

    Radical Axis of 3 circles...

    Can someone help me with this. Suppose you have 3 circles and you find the radical axis of each of these. Apparently the 3 radical axes intersect at a unique point. Q1: why? and Q2: Apparently there is a unique circle ( centre point intersection of radical axes) which is orthogonal to each...
  10. X


    3. A small radio transmitter broadcasts in a 50 mile radius. If you drive along a straight line from a city 60 miles north of the transmitter to a second city 70 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter? I am completely lost on...
  11. G

    Intro to Circles Problem (Circles, Points, Substituion, Graph of the equation)

    Center of the circle is O=(2,4). Verify by substitution that point A=(5,8) is on the circle that is the graph of the equation (x-2)^2+(y-4)^2=25
  12. S

    Plane defined by Circle

    Given three points that are not colinear, how do you define a plane such that the circle intersecting these three points lies on the plane? Please define the plane as a function f(x,y) = \alpha x + \beta y + \gamma.
  13. J

    Help with unit circles

    Hi. I am having trouble proving that cos(theta + pi/2) = -sin theta, using a unit circle. I was hoping someone could help me out here using a unit circle diagram to show. Thanks, Jono
  14. C

    Circles related angles and segments.

    Hey Guys, I'm having some trouble with this problem. so far I know that XY = 10. I looked at the whole triangle first. Triangle XYZ. I know that XZ is 6 so I applied the pythagoreans theorem which got me YZ = 8. From this step I don't know what to do. I've tried looking at it different ways...
  15. G

    Two non-intersecting circles...

    Two non-intersecting circles C1, containing points M and S, and C2, containing points N and R, have centres P and Q where PQ=50. The line segments [MN] and [SR] are common tangents to the circles. The size of the reflex angle MPS is α, the size of the obtuse angle NQR is β, and the size of the...
  16. N

    Area between two circles

    Find the area of the region between the circles x^2 + y^2 = 4 and x^2 + y^2 = 4x My attempt at the solution: I found the points of intersection are at (1,-sqrt(3)) and (1, sqrt(3)) Then I solved for x in each equation: x=sqrt(4-y^2) , x=sqrt(y^2+4) + 4 This is where I get stuck. I don't know...
  17. W

    Circles and Angles

    I'm hoping that someone can give me some help with the following problem: O is the centre of the circle (show on the attachment to this post) and AB is parallel to CD. Find the angles labelled x and y. With a bit of cheating I was able to find that x = 32o and y = 58o but my questions is 'why'...
  18. R

    Equations of Circles

    Circle C1 has points B(4,2) and E(10,12) on its circumference. Equation of circle and radius are not known. Show that Circle C1 has its centre O at (2,10) Please advise (I read that you can find the centre with 3 points, or 2 points + radius known, but this case has no radius?)
  19. U

    different circles

    If three different circles are drawn on a piece of paper, at most how many points can be common to all three? A) Non B) one C) two D) three E)six E is the correct answer I could get four...but I cant get six at all! So is that enough reason to choose E?
  20. M

    Identifying Ellipses,Circles and Parobolas w/Picture

    How can you tell if its an ellipse, circle or a parobola? I noticed that the Parobla only has one term with a degree of 2 . I noticed that the circle has same coefficients with their terms like y=x^2 +y^2 another example of cirlce y=9x^2 +9x^2 The Ellipse has different number coefficents...