Friday, January 20, 2017

Geometry Problem 1308 Quadrilateral, Diagonal, Triangle, Incircle, Tangent Line, Sides, Measurement

Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

Details: Click on the figure below.

Geometry Problem 1308 Quadrilateral, Diagonal, Triangle, Incircle, Tangent Line, Sides, Measurement.

Posted by Antonio Gutierrez at 9:05 AM
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2 comments:

  1. Peter TranJanuary 20, 2017 at 12:50 PM

    Let e= AC and 2p1= perimeter of triangle ABC and 2p2= perimeter of triangle ACD
    In triangle ACD we have AF= p2-c= ½(d+c+e)-c
    In triangle ABC we have AE= p1-b= ½(a+b+e)- b
    X= AF-AE=½(d+c+e)-c-(½(a+b+e)- b)= ½(b+d-a-c)

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  2. Sumith PeirisJanuary 20, 2017 at 9:07 PM

    Let the points of tangency on AB, BC, CD, DA respectively be X,Y,U,V.

    If BX = BY = p, AX = AE = a-p, CF = CU = b-p-x.
    So DU = DV = c-b+p+x.
    Hence AV = d + c - b - p - x = AF = a-p+x

    So 2x = d + c - b - a.

    Sumith Peiris
    Moratuwa
    Sri Lanka

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