Sunday, April 25, 2010

Problem 437: Tangent Circles, Diameter, Chord, Perpendicular, Congruence

Proposed Problem
Click the figure below to see the complete problem 437 about Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.

Problem 437.<br />Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.
See also:
Complete Problem 437

Level: High School, SAT Prep, College geometry

Posted by Antonio Gutierrez at 12:34 AM
Labels: , , , , , , ,

2 comments:

  1. c .t . e. oApril 25, 2010 at 2:22 AM

    ▲ANE ~ ▲AMH => AN/AM = AE/AH (1)
    ▲AFE ~ ▲AGH => AF/AG = AE/AH = AC/AB (2)
    from (1) & (2)
    AN/AM = AC/AB
    (3)
    PK perpendic to AB
    ▲APK ~ ▲ADE => AP/AD = AC/AB (4)
    from (3) & (4)
    AN/AM = AP/AD ( AM = AD from P436 )

    AN = AP
    ------------------------------------------

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  2. Sumith PeirisApril 28, 2019 at 7:55 AM

    AN.AM = AE.AC, CENM being concyclic
    AM^2 = AE.AB

    Dividing, AN/AM = AC/AB = AP/AD since CP//BD

    Since AD = AM as proved in Problem 436, AP = AN


    Sumith Peiris
    Moratuwa
    Sri Lanka

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