Saturday, December 12, 2015

Geometry Problem 1172: Cyclic Quadrilateral, Circle, Secant, Triangle, Similarity, Metric Relations

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

Click the figure below to view more details of problem 1172.

Online Math: Geometry Problem 1172: Cyclic Quadrilateral, Circle, Secant, Triangle, Similarity, Metric Relations.

2 comments:

  1. Let EC = y.

    From similar triangles, we have
    x/(y+c) = y/(x+a) = b/d

    dx = by + bc
    dy = bx + ab

    dx - by = bc
    bx - dy = -ab

    By solving, we have
    x = b(ab + cd)/(d² - b²)

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  2. One of the easiest for some time Antonio!

    Also EC = b(ad+bc)/(d^2-b^2)

    We can write similar expressions for the diagonals again using similar triangles and deduce using Ptolemy that

    BD^2 = (ac+bd)(cd+ab)/(ad+bc)

    AC^2 = (ad+bc)(ac+bd)/(ad+bc)

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