Saturday, March 23, 2019

Geometry Problem 1428: Intersecting Circles, Tangent Line, Triangle, Square, Area

Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

Details: Click on the figure below.

Geometry Problem 1428: Intersecting Circles, Tangent Line, Triangle, Square, Area, Tutoring.
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3 comments:

  1. c.t.e.oMarch 23, 2019 at 4:33 PM

    Extend EA to T, CA to P, (P, T on circle O)
    Draw OG ꓕ AP => OP = AC/2

    ReplyDelete
  2. Peter TranMarch 23, 2019 at 6:12 PM

    https://photos.app.goo.gl/z8XEgvg4x6Eq1rML8

    see sketch for position of points M and N
    note that OAQ is isosceles right triangle
    Let M and N are the projection of Q and O over AC
    Triangle ONA congruent to AMQ ( case ASA)
    So ON= AM= ½. AE
    Area S= ½. ON.AC= ½ x ½ x AC. AC= ¼ S1

    ReplyDelete
  3. Sumith PeirisMarch 23, 2019 at 9:32 PM

    Extend AQ to meet Circle Q at X. Drop a perpendicular from C to OA meeting it at Y.
    Let OA = AQ= QX = r and let AC = y

    Tr.s ACY and ACX are similar since < XAY = < ACX = 90

    So y/2r = h/y and h = y^2/2r = S1/2r i.e. S1 = 2rh …(1)
    But S = rh/2...(2)

    From (1) and (2) S1 = 4S

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete

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