Sunday, April 2, 2023

Crack the Code of Geometry Problem 1532: How to Find the Angle in a Square with a Tangent Semicircle

Geometry Problem 1532. 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 1532: Crack the Code of Geometry Problem 1532: How to Find the Angle in a Square with a Tangent Semicircle.

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5 comments:

  1. Let M is the midpoint of AD
    since TD ⊥MC => ∡ (CTD)=∡ (CDT)=∡ (CMD)
    ∡ (CMD)= atan(CD/MD) =atan(2)~63.43 degrees

    ReplyDelete
  2. Let O be the mid point of AD.
    Then OTCD is a kite and < TCO = < DCO = arctan (1/2).
    So ? = 90 - arctan (1/2)

    ReplyDelete
    Replies
    1. 90 - arctan (1/2) is the same as arctan(2) = 63.4 degrees approximately

      Delete
  3. BT/AT = sqrt2 is another result from this problem

    ReplyDelete