Monday, March 6, 2023

Geometry Problem 1521: Unlock the Secret to Finding the Measure of an Angle in a Triangle with Two Sides as Diameters of Circles. Difficulty Level: High School.

Geometry Problem 1521. 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 1521: Unlock the Secret to Finding the Measure of an Angle in a Triangle with Two Sides as Diameters of Circles. Difficulty Level: High School.

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5 comments:

  1. DBE = 70° (It will be explained on the sketch)

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    1. https://photos.app.goo.gl/KzkMvaHgbfKy5cqt7

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    2. Again one comment is deleted : https://photos.app.goo.gl/CxQ2Xvm1BvtF8zg19

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  2. Let <QBD = < QDB = p and let < OBE = < OEB = q

    In Triangle OQB,
    (p+p-40) + (q + q - 40) = 140
    So p + q = 220/2 = 110

    Hence < DBE = p + q - 40 = 70

    Sumith Peiris
    Moratuwa
    Sri Lanka

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  3. https://photos.app.goo.gl/kYPKJjPWmLn4TNQd7

    Note that BOE and BQD are isosceles triangles
    See sketch for angles d, o, q and e
    We have d= 90-½.q
    And e=90-½. o
    So d+e= 180-½(q+o)
    But q+o= 180- ∡(ABC)= 140
    So d+e= 110
    And∡(DBE)= 180-(d+e)= 70

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