Inscribed triangle

This is based on a theorem "ANGLE IN A SEMI-CIRCLE IS A RIGHT ANGLE"
We learn that in High-school.

Following is the proof.

Refer attached diagram also.

1) We can split the triangle in two by drawing a line from the centre of the circle to the point on the circumference our triangle touches.

2) We know that each of the lines which is a radius of the circle (the green lines) are the same length. Therefore each of the two triangles is isosceles and has a pair of equal angles.

3) But all of these angles together must add up to 180°, since they are the angles of the original big triangle.

Therefore x + y + x + y = 180, in other words 2(x + y) = 180.
and so x + y = 90. But x + y is the size of the angle we wanted to find.

Thus, for any angle inside a semi-circle, it is a right angle.
This a theorem and is universally true.