Find the angle

Geometry Level 3

5


The answer is 35.

Aly Ahmed by Aly Ahmed , 34, Egypt

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1 solution

We have: A E 2 = A F × A B = A D × A C = A G 2 ⇒ A E = A G = A F ⇒ A AE^{2}=AF \times AB = AD\times AC =AG^{2} \Rightarrow AE=AG=AF \Rightarrow A is circumcenter of ⊙ E G H ⇒ ∠ E G H = 9 0 ∘ − ∠ A E H = 3 5 ∘ Q . E . D \odot EGH \Rightarrow \angle EGH = 90^{\circ}- \angle AEH = 35^{\circ} \boxed{Q.E.D}

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