Saturday, March 11, 2023

Geometry Problem 1525: Unveiling the Secrets of an Equilateral Triangle in Right Triangle Geometry: Finding the Midpoint Distance between Segments. Difficulty Level: High School.

Geometry Problem 1525. 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 1525: Unveiling the Secrets of an Equilateral Triangle in Right Triangle Geometry: Finding the Midpoint Distance between Segments. Difficulty Level: High School.

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5 comments:

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    1. https://photos.app.goo.gl/Qt4wWUDARG6fzTrbA

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    2. Why the sketch is deleted

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    3. I'm sorry to hear that your sketch was deleted from the blog. there may have been a technical issue that led to the deletion. I have just re-sent your post to the blog. Thank you.

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  2. Let P be the mid-point of CD

    In Triangles BMN & CPN,
    < MBN = < PCN (= A - 30)
    BN = NC (since N is the circumcenter of right triangle ABC)
    BM = MP (since Triangle DPM is equilateral)
    So Triangles BMN & CPN are congruent SAS

    Now using the midpoint theorem in Triangle ACD,
    MN = NP = AD/2 = 6/2 = 3

    Sumith Peiris
    Moratuwa
    Sri Lanka

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