1. J

    Nested Tangent Circles

    I need help with the following problem. All circles are tangent to each other, if the radius of the small circle is r then what is the radius of the largest one in terms of r? I can visually see that it is 6r, but I want to know why. I've tried constructing several triangles in the picture...
  2. S

    Co-ordinate Geometry-Cirlcles

    Through a fixed point (h,k) secants are drawn to the circle x2 + y2 =a2. The locus of the mid points of the secants intercepted by the given circle is ....?? My Answer: x2 + y2 = 2(hx + ky) Book's Answer : x2 + y2 = (hx + ky) Here's what i did: Maybe the book is correct but i can't...
  3. S

    Is it possible to draw triangles and circles using latex?

    Hi, Is it possible to draw these shapes using latex? Thanks.
  4. J

    HELP! D.E.of a family of circles tangent to the x-axis :))

    Find the Differential Equation of Family of Circles Tangent to the X-axis! Thank you to those who will help :)))
  5. G

    Circles and Chords

    Below, I have posted a question and a solution I was provided. The problem is that I don't understand how the part bordered by AAA was arrived at. Specifically \sqrt{m^2+1}, & why it's simply multiplied against |3m+4|? After multiplying that expression, I end up with (3m^2+24m+16)(m^2+1)=20...
  6. G

    Circles and Chords

    Having a bit of trouble with this one. Can anyone help me out? Many thanks. Q. C is a circle with centre (-1, -4). The midpoint of a chord of length 2\sqrt{5} is (2, 0). Find the length of the radius of C. Attempt: Perpendicular distance [bc] from centre c to x-axis is 4, Let |ab| = 1/2...
  7. A

    fun circle challenge problem

    found this problem today and I've been struggling to wrap my head around it. I find it really interesting and if someone would like to give their two cents, I invite you to do so. heres the problem: Two circles of radius R are tangent to each other. A line is drawn tangent to both circles...
  8. Y

    Finding the area of shaded region between two circles (picture included)

    Find the area of the shaded region in terms of pi. O and P are the centers of the circle
  9. G

    Infinite Number of circles

    On a straight line ℓ, we have an infinite sequence of circles Γn, each with radius 12n, such that Γn is externally tangential to the circles Γn−1,Γn+1 and the line ℓ. Consider another infinite sequence of circles Cn, each with radius rn, such that Cn is externally tangential to Γn,Γn+1 and ℓ...
  10. S

    Need Help with a Few Problems Please

    1. Determine if the graph of the equation y = 16 - x^2 is symmetric with respect to: a) the x-axis (yes or no, w/ brief explanation) b) the y-axis (yes or no, w/ brief explanation) c) the origin (yes or no, w/ brief explanation) d) Find the x-intercept(s). e) Find the y-intercepts(s). 2. Given...
  11. E

    Equilateral triangle and inscribed circles, mixed polygons, just my favorite...

    There is an equilateral triangle that is shaded except for the inscribed circle smack in the middle. The radius is 8 and I have to find the shaded area's area.
  12. NatalieSv94

    Positions of points in intersecting circles (DIFFICULT)

    Hi! here is the task I was talking about in my introductory thread I just posted a few minutes ago. I got this task yesterday and I have no idea how to even start with it. Here is an image of the task. I read it 100 times but I still don't know what to do! (Crying)
  13. NatalieSv94

    Positions of points in intersecting circles (DIFFICULT)

    The thread's moved Hi, I moved this thread since I though I uploaded it at the wrong place. So you can find it here instead: and pleeeeeeeeaaaaaaaaase heeeeeeeeeeeeeeeelp meeeeeeeeeeee! :P...
  14. T

    How many circles of diameter d on average in area of size A?

    Hi, I have an unlimited large plane. I am trying to calculated how many circles with a certain diameter d can fit into any square of size SxS on the plane. I think this should be the maximum density. So the question is NOT "How many circles can I fit into square of size x?", as it does not...
  15. B

    Help with a few circles......

    Hey guys new to the forum hoping you can fix my stupidity. SO the first problem asks to find the equation of the circle whose center is on the y axis and that contain the points (1,4) and (-3,2). Give the center and the radius. I can find the radius and write the equation I am just struggling to...
  16. W

    At least two circles tangent to y axis with nonempty intersection

    Hi. Here is a problem I've been trying to solve for some time now. Maybe you could help me. We have two sets \mathcal {Q} is a set of those circles in the plane such that for any x \in \mathbb{R} there exists a circle O \in \mathcal {Q} which intersects x axis in (x,0). \mathcal {T} is a set...
  17. B

    Questions about points on the surface of a sphere & great circles...

    Hi, Is it true the for any 2 points on the surface of a sphere it is possible to draw a great circle that passes through both points? I have a few follow up questions about this but will wait for a response before I launch into unfounded conjecture :) B
  18. E

    Help with Circles and Revolutions

    There are 1760 yards in a mile. A certain wheel makes 17,600 revolutions in 40 miles. What is the number of yards in the radius of the wheel? Give your answer as a decimal to the nearest tenth of a mile.
  19. M670

    One more time with Circles

    Find the coordinates of the center and radius of the circle. x^2+y^2-8x+10y=-5 So I like to rewrite it x^2-8x+y^2+10y=-5 then I write it as the standard circle equation (x-h)^2+(y-K)^2=r^2 So If I did this right I should have (x-4)^2+(y+5)^2=-46 and then my (h,k) is (4,-5) and r=\sqrt46...
  20. C

    Classical question about constant gaussian curvature and geodesics circles.

    Hi everyone! I am having problem in a classical question, I have to prove that in a regular surface with constant gaussian curvature the geodesics circles have constant geodesic curvature. I don't konwm how to start... thanks!