Given $AB$ is diameter, $C$ and $D$ lie on circumference, $AB = 15cm$, $AC = 12cm$, $BD = 9cm$, find area of quadrilateral ABCD.
Note that the points $O$ and $Q$ were not in the original diagram.
I guessed that $\triangle ABC$ is congruent to $\triangle ABD$, computed the area, and it actually came out to be the correct answer! But I have no idea how they can be proved congruent. And so, I need help in proving those triangles congruent.