Reading the question carefully, "<span>He draws the diameter of the circle through center P using a straight edge. Next he opens his compass to a width equivalent to the radius of the circle." - that implies that Mateo is still in the process of drawing the circle by which the equilateral is inscribed to.
The next steps should be: *He should draw the upper and lower arcs using the compass opened to a width equivalent to the radius of the sircle. *Make a vertical diameter using centroid P as basis. *Draw two right triangles facing the opposite directions using the top most point by which the vertical diameter of the circle touches the top most circumference of the circle.
Doing these steps, Mateo will be able to draw an equilateral triangle inscribed in a circle. </span>
It is a right triangle because a 3, 4, 5 triangle is always a right triangle. it is because it is a Pythagorean Triple. all the sides are whole numbers
