For questions about general quadrilaterals (including parallelograms, trapezoids, rhombi) and their properties.

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### Prove that $\frac{AB}{AE} + \frac{AD}{AG} = \frac{AC}{AF}$ in parallelogram $ABCD$, where $E$, $F$, $G$ are points on a line intersecting the sides

Let $ABCD$ be a parallelogram. A line meets segments $AB$, $AC$, $AD$ at points $E$, $F$, $G$, respectively. Prove that $\frac{AB}{AE} + \frac{AD}{AG} = \frac{AC}{AF}$. So recently I've been assigned ...
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### Kites and Trapeziums and Circle

Let there be a circle with center O and let A, B, C, D, be points on the circle such that O is in the interior of quadrilateral ABCD. Construct the four tangents at A, B, C, D. Let P be the ...
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### Find the largest diagonal of a parallelogram if the area is known

The original question: In a parallelogram, the length of one diagonal is twice of the other diagonal. If its area is $50\text{ sq. metres}$, then the length of its bigger diagonal is... A) ...
A quadrilateral $ABCD$ has $∠BAD = ∠BCD$ and diagonal $AC$ bisects diagonal $BD$ at $P$. Is it necessarily a parallelogram? If not, give an example of such a quadrilateral. Provide proof. I was ...