Playing With Triangles

Geometry Level pending

In acute-angled triangle $ABC$ , Let $D$ be the foot of the altitude from $A$ , and $E$ be the midpoint of $BC$ . Let $F$ be the midpoint of $AC$ . Suppose $\angle BAE = 40$ . If $\angle DAE = \angle DFE$ ,what is the magnitude of $\angle AEF$ in degrees?

The answer is 40.

1 solution

Md Zuhair
Aug 4, 2016

Now After drawing the figure we will see that $EF \\ AB$ . And $AED and EFD are concylic$ . Hence $\angle FDA$ = $\angle AED$ . And $\angle AED$ = 40 as $AB \\ EF$ [ E and F are midpoints so by Midpt. Theorem.

Playing With Triangles

The answer is 40.

1 solution

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