Sunday, February 26, 2023

Geometry Problem 1514: Discover the Secret to Finding Distances in Regular Hexagons with Interior Squares. Difficulty Level: High School.

Geometry Problem 1514. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

Details: Click on the figure below.

Geometry Problem 1514: Discover the Secret to Finding Distances in Regular Hexagons with Interior Squares. Difficulty Level: High School.

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To post a solution to this problem click Comment underneath the post, or click into the line that says, “Enter Comment.” Type what you want to say and press Publish to post your solution.

7 comments:

  1. GK = 6V2 ( square root) It will be explained in the sketch.

    ReplyDelete
    Replies
    1. In Tr. GKH, < GKH > 90 so GH > GK and so GK < 6 but you say GK = 6.sqrt.2 > 6. Hence the answer is incorrect

      Delete
    2. https://photos.app.goo.gl/4AzheNU5tkxHPCtt8

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    3. This and some of previous are for beginners (students) : https://photos.app.goo.gl/upPuhDvxkQ8sj54B8

      Delete
  2. Since < AFE = 120 and < MFE = 90, <AFM = 30.
    So <GFM = < GFA - < AFM = 45 - 30 =15 and < GFK = < NFM - < GFM = 45 - 15 = 30.

    Hence Tr. GFK is 30-60-90 and so
    GK = GF/2 = (6.sqrt.2)/2 which is the same as 6 / sqrt.2

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete
  3. Some interesting results

    1) Tr.s ABG, AFM, FHE, END, GHM, MHN are all congruent and isosceles 75-30-75
    2) B,G,K are collinear
    3) Tr.s FEN & BKF are right isosceles

    ReplyDelete
  4. Not for post, just take a look, if square ASTB is added, then P, M, S are interesting points. https://photos.app.goo.gl/8xKYnMSYxAXuR9Jw7

    ReplyDelete