Question 44
The diagonal $BD$ of the quadrilateral $ABCD$ divides this quadrilateral into an acute triangle $ABD$ and an equilateral triangle $BCD$. Let $O$ be the circumcentre of the triangle $ABD$. Prove:
a. if the triangles $ABD$ and $OCD$ are congruent, then $AB \perp BC$;
b. if $\angle CBA = 90^\circ$, then the triangles $ABD$ and $OCD$ are congruent.
a. if the triangles $ABD$ and $OCD$ are congruent, then $AB \perp BC$;
b. if $\angle CBA = 90^\circ$, then the triangles $ABD$ and $OCD$ are congruent.