Question 28
Let $A',B'$ be the feet of the altitudes from $A,B$, respectively, of acute triangle $ABC$ with $AC\ne BC$. A circle $k$ passes through $A',B'$ and is tangent to side $AB$ at $D$. If triangles $ADA'$ and $BDB'$ have equal areas, prove that $\angle A'DB'=\angle ACB$.