# Find angle in a figure involving a scalene triangle

$\triangle ABC$ is a scalene triangle and $\overline {AM}$ is the median relative to the side $\overline {BC}$. A circumference of diameter $\overline {AM}$ intersects by the second time sides $\overline {AB}$ and $\overline {AC}$ at points P and Q, respectively, both different from A. Assuming that $\overline {PQ}$ is parallel to $\overline {BC}$, find the measure of angle $\angle BAC$.

Background: I'm a 9th grader who has some experience in math contests. This is question 5 (level 2), from the 2013 Brazilian Math Olympic (OBM). The answer was not given, and I believe that it's impossible to find a solution, given that $\triangle ABC$ cannot be scalene in the conditions given by the question, but I'm not sure.

My attempt:

(1)Using the information given in the question and considering that the circumference intersects the sides of the triangle is at point A, I came up with

(2)$\overline {CB}$ is tangent to the circle, so: $$\angle AMB=\angle AMC=90°$$

(3)Point M is the midpoint of $\overline {BC}$, so: $$\overline {CM}=\overline {BM}$$

Using (1), (2), and (3), I can conclude that $\triangle ABC$ is isosceles, which contradicts the statement in the question, in which it is stated that $\triangle ABC$ is scalene.

Question: Did I interpret something wrong? Is it impossible to find a scalene triangle that complies with the statement? Any help is appreciated.