Friday, April 23, 2010

Problem 436: Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.

Proposed Problem
Click the figure below to see the complete problem 436 about Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.

Problem 436.<br />Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.
See also:
Complete Problem 436

Level: High School, SAT Prep, College geometry

8 comments:

  1. ▲AFE ~ ▲AGH => AF/AG = AE/AH (right tr & comm ang A)
    ▲AGB ~ ▲AFC => AF/AG = AC/AB (right tr & comm ang A)
    =>
    AE/AH = AC/AB =>
    AB∙AE = AC∙AH =>
    (AE + EB)∙AE = (AH+HC)∙AH
    AE² + EB∙AE = AH² + HC∙AH
    AE² + ED² = AH² + MH² (ED², MH² from euclid Theorem)
    AD² = AM²

    AD = AM
    ---------------------------------------------

    ReplyDelete
  2. Problem 436
    Is AG^2/AF^2=(AH.AB)/(AE.AC),but AG^2/AF^2=AH^2/AE^2=(AH.AB)/(AE.AC) so AH/AE=AB/AC. But AD^2/AM^2=(AE.AB)/(AH.AC=1.Therefore AD=AM.
    APOSTOLIS MANOLOUDIS 4 HIGH SHCOOL OF KORYDALLOS PIRAEUS GREECE

    ReplyDelete
  3. By easy angle chase we get tr. ADG ~ tr. AFD and tr. AMG ~ tr. AFM, from their similitude inferring AD^2=AF.AG=AM^2, done

    ReplyDelete
  4. Greetings to u all Gogeometers from Sri Lanka as we try to come to terms with what has happened on Easter Sunday

    May God help us

    < FCA = < GBA = < AGH hence AM^2 = AF.AG

    <ADE = < ABD = < AGD hence AD^2 = AF.AG

    So AD = AM

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete
  5. Dear Sumith,
    My deepest condolences to you and your country

    ReplyDelete
    Replies
    1. Thank u Antonio for your concern.

      My wife and I were on the way to churches 100 km North of Colombo when the news came. Pls pray for us.

      Delete
  6. Dear Sumith

    My condolences to your country. I remember these victims in my prayers

    Peter tran ,
    California, usa

    ReplyDelete