1. G

    find the coordinates of the 2 sides of a chord

    If I have the circle's equation including r and circle's origin coordinates. And I have the coordinates of a point M in the middle of a chord which splits the chord into 2 equal parts. Then how do I find the coordinates of each point in each side of the chord?
  2. A

    Condition for a chord to subtend a right angle at the center.

    This is a problem from SL Loney's The elements of coordinate geometry. The problem is:- Find the condition that the chord of contact of tangents from the point (x', y') to the circle x^2 + y^2 = a^2 should subtend a right angle at the center.. What I have thought is that the equation to the...
  3. V

    Height of a Circle's segment

    Given the chord length and area of a segment of circle, how can we find the height of the segment?
  4. D

    Finding Chord length given arc length and arc height?

    I'm not sure this is possible but I'm in the process of building a tent and am trying to get two curved surfaces to meet. How can I find the length of a Chord of a circle if I have the Arc length and Arc height? I'm not sure this is possible without the radius but maybe there is...
  5. P

    Maximum Chord Angle

    1. What is the maximum chord angle in the circle? 2. What is the maximum chord angle that one of its side is diameter?
  6. M

    Arc Length given Chord Length & Height

    I got a formula for arc length from this page s = Arcsin(c / (h + c^2 / 4h)) X (h + c^2 / 4h) given c = 163' & h = 7' I do s = Arcsin (163 / (7 + 163^2 / 4 X 7)) X (7 + 163^2 / 4 X 7) s = Arcsin (163 / 955.89) X (955.89) s = Arcsin...
  7. M

    Circle - tangent or chord?

    Hi All, I'm having a little difficulty with this problem. Any help would be appreciated. Show that the line 2y + x = 31 is a tangent to the circle x^2 + y^2 - 6x - 8y - 55 = 0 and determine point of contact. When I insert x = 31-2y into the circle equation I get 5y^2 - 124y + 720 = 0 and...
  8. S

    Find the radius of the congruent circle from equal arc and equal chord length

    Dear All I have been trying this state math contest for several times. Please see the attachment. In the problem, they gave equal arc length and equidistant chord from center. As far i did, this inner triangle will be equilateral. But how can i know the chord length? Please give me a...
  9. A

    how many degrees to a chord?

    How many radians form the circular segment for any given chord length of a circle with constant radius? Draw a circle and a chord. Connect the endpoints of the chord to the centre of the circle. What is the central angle? Is there a relationship between the radius length and chord length...
  10. R

    Looking for a formula to calculate a chord length

    I am sorry to post such a lame question to all you fine people, but you either know or you don't...and I don't. What I am looking for is a formula that calculates the length X shown in the picture attached. I am given 'Y' dimension and Diameter 'D' only
  11. T

    Help with the proper Calculation for Chord length

    Can someone help me figure out the formula for solving Chord DE (see attachment)? The two formulas I have been trying up till now (with two different results) are... .50*sin(15+acos((.5-2*.02)/.5) = .3083 or .50*sin(15+acos((.5-.02)/.5) = .2594 any help will be appreciated. Also, this...
  12. D

    Equation of the common chord of 2 circles

    I found this question: What is the equation of the common chord of the circles x²+y²=16 and x²+y²-8x-8y+16=0? In the answer, they simply plugged in x²+y²=16 in the second equation to get 16-8x-8y+16=0, and then ==> y=-x+9. They say that's the equation of the chord. I don't understand...
  13. W

    Measuring central angle of a curve given arc and chord lengt

    Hello math experts, thanks for giving me the opportunity to post here. My maths education is limited to a 16 yr old's so your help is much appreciated. In my attachment, I have measured A, B and C in 112 different subjects. Using these measurements, I hope to come up with an approximate index...
  14. B

    how do I calculate radius of a circle, from chord length? ,,

    How do I calculate the radius of a circle, from chord length and sagitta? My old brain is creaky, and it seems like that's enough known variables to find that section's angle, and the radius. Gratitude in advance
  15. B

    Finding centre of a circle from a chord

    Hi all, I've been having some difficulty working out the centre of a circle for a program I'm making. I only know three things about the circle - the chord start and finish coordinates and the angle of the circle it represents (subtends?) (Basically points A and B and the angle as shown in this...
  16. R

    Circle Chord

    Points D, E, and F lie on a circle with center at O. EH is tangent to the circle at E. Chords EF and DJ intersect at K such that DJ is parallel to EH. If DE = 180 and EK = 108, find KF. It seems that in order to find the solution you need to use Power of a Point and notice that OH is...
  17. E

    A Circle and Chord Property

    Let OA \perp MN, P, Q are determined by A, B,C,D,E on \odot O as shown. Show that \overline{PA} = \overline{QA}
  18. D

    P is a midpoint of a chord AB

    I've been trying to do this problem for ages with no avail. P is a midpoint of a chord AB of a circle. XY is a chord containing the point P. The tangents at X and Y meet AB extended at M and N respectively. Prove that AM = BN
  19. A

    Chord length

    Hello All, Urgent requirement. Formulae for length of the chord in hyperspace given diameter and lenth of the arc in the normal space. Thanks In Advance, Aakash