Home > Triangles > An Intriguing Geometry Problem – Triangle problem

An Intriguing Geometry Problem – Triangle problem

Let ABC be an isosceles triangle (AB=AC) with BAC = 20°. Point D is on side AC such that DBC = 60°. Point E is on side AB such that ECB = 50°. Find, with proof, the measure of EDB.

For more about this question go to Berkeley Math Circle. You can read history of this question and about solutions. Picture is taken from thinkzone.wlonk.com .

SOLUTION :

You can draw few lines find isosceles and equaliteral triangles and find kite. Or you can use law of sines, or other methods.

sin(20° + x) = 2 cos 40° sin x  If you get this, then you are one step away from answer.

This is graph of two functions f(x)=sin(20° + x) & g(x)=2 cos 40° sin x . Intersection point is x≈ 0.52 and this is ≈30° . (I used Bagatrix Graphing Solved)

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  1. October 4, 2011 at 14:13
  2. October 31, 2011 at 11:43

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