Saturday, November 23, 2024

Geometry Problem 1582: Prove That Angles AFD and AEF Are Equal in This Secant Problem.

Challenging Geometry Puzzle: Problem 1582. Share your solution by posting it in the comment box provided.
Audience: Mathematics Education - K-12 Schools, Honors Geometry, and College Level.

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Illustration of Geometry Problem 1582

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3 comments:

  1. In Circle Q,
    Let < ACF = < AEF = x
    Let < AFB = y
    Let < FAE = < FCE = z

    So from Circle O, < ADB = < ACE = x + z
    But in Triangle ADF, < ADB = x + y
    Hence y = z and
    < AFD = < AEF

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete
    Replies
    1. It follows that AF is tangential to Circle BCF at F

      Sumith Peiris
      Moratuwa
      Sri Lanka

      Delete
    2. ... and to circle (FED) as well!

      Delete