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Geometry Level 3

In a triangle A B C ABC , ∠ B C A = 9 0 ∘ \angle BCA=90^\circ . Points E E and F F lie on the hypotenuse A B AB such that A E = A C AE =AC and B F = B C BF=BC . Find ∠ E C F \angle ECF in degrees.


The answer is 45.

Puneet Pinku by Puneet Pinku , 20, India

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1 solution

Abdullah Ahmed
Aug 31, 2016

let ∠ B C E \angle BCE = x x , ∠ E C F \angle ECF = y y and ∠ F C A \angle FCA = z z

Now, as B C BC = B F BF and also A C AC = A E AE

So, ∠ C F E \angle CFE = x + y x+y and ∠ C E F \angle CEF = y + z y+z

Now, y y + x x + y y + y y + z z = 180 180

or, 2 y 2y = 180 180 - ( x + y + z x+y+z ) [x+y+z=90]

so y y = 180 / 2 180/2 = 45 45

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