Question 6
A circle $\omega$ is inscribed in a quadrilateral $ABCD$. Let $I$ be its center. Suppose that
$$(AI+DI)^2+(BI+CI)^2=(AB+CD)^2.$$
Prove that $ABCD$ is an isosceles trapezoid.
Proposed by Zuming Feng (credited in the supplied source).
$$(AI+DI)^2+(BI+CI)^2=(AB+CD)^2.$$
Prove that $ABCD$ is an isosceles trapezoid.
Proposed by Zuming Feng (credited in the supplied source).