Geometry

posted by .

A circle \Gamma cuts the sides of a equilateral triangle ABC at 6 distinct points. Specifically, \Gamma intersects AB at points D and E such that A, D, E, B lie in order. \Gamma intersects BC at points F and G such that B, F, G, C lie in order. \Gamma intersects CA at points H and I such that C, H, I, A lie in order. If |AD| =3, |DE| =39, |EB| = 6 and |FG| = 21 , what is the value of |HI|^2 ?

  • Geometry -

    From the secant-secant rule,

    FB*21 = 6*39, so FB=78/7
    AD+DE+EB = 3+39+6 = 48
    CG+21+FB = 48, so CG = 111/7

    CH*HI = CG*CF = 111/7 * 258/7 = 28638/49
    AI*HI = 3*39 = 117
    AI+IH+HC = 48

    117/HI + HI + 28638/49HI = 48

    now "just" solve for HI

    The fractions look nasty, so you better check my arithmetic.

  • Geometry -

    Oops. I was multiplying the wrong segments:

    FB(FB+21) = 6*45
    FB = 9
    FB+FG+CG=48 so CG = 18

    CH*(CH+HI) = 18*39 = 702
    AI*(AI+HI) = 3*42 = 126
    AI+HI+CH = 48

    Things look better now

  • Geometry -

    Yes, solving gives HI^2= 792.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Bio

    of the following, the best conclusion concerning the difference between the S phases for beta and gamma is that: a. gamma contains more DNA than beta b. beta and gamma contains the same amout of DNA c. beta contains more RNA than gamma …
  2. physics

    Find Beta and Gamma for an electron that has a kinetic energy of 6.00 keV. â?
  3. physics please help

    Find Beta and Gamma for an electron that has a kinetic energy of 6.00 keV. gamma = KE/MoC^2 + 1 Beta = 1/gamma^2 + 1 gamma = 1.011723381 Beta = 1.9769592 I am getting gamma right but I am getting Beta wrong what I'm I doing wrong?
  4. geometry

    In a triangle ABC,E and F are the mid-points of AC and AB respectively. The altitude AP to BC intersects EF at Q.Prove AQ =PB.
  5. Physics

    Gamma-ray bursters are objects in the universe that emit pulses of gamma rays with high energies. The frequency of the most energetic bursts has been measured at around 3.0 × 10 21 Hz. The speed of light is 3 × 10 8 m/s. What is …
  6. Physics: Formulas

    the momnetum of a gamma photon is determined by the equation p=h/lambda. for the decay of iodine-131 the relationship between the magnitude of the momentum of the gamma ray photon and the mangnitude of the momentum of the beta particle …
  7. circle geometry

    Circles Γ1 and Γ2 intersect at 2 distinct points A and B. A line l through A intersects Γ1 and Γ2 at C and D, respectively. Let M be the midpoint of CD. The line MB intersects Γ1 and Γ2 again at E and …
  8. Geometry

    ABCD is a trapezoid with AB < CD and AB parallel to CD. \Gamma is a circle inscribed in ABCD, such that \Gamma is tangent to all four sides. If AD = BC = 25 and the area of ABCD is 600, what is the radius of \Gamma?
  9. GEOMETRY......circle

    Circles Γ1 and Γ2 intersect at 2 distinct points A and B. A line l through A intersects Γ1 and Γ2 at points C and D, respectively. Point E is the intersection of the tangent to Γ1 at C and the tangent to Γ2 …
  10. Geometry

    Please answer at least one . PLEASE 1. Triangle XYZ has a right angle at Y. V,W are on XZ such that XV=XY. WZ=YZ, find ANGLE VYW . 2. STUVWXYZ is a regular octagon. Find SW/ TZ. 3. The interior angles of a convex polygon form an arithmetic …

More Similar Questions