In a semicircle
is the diameter of a semi-circle.
is a point on the circumference.
What is the measure of angle
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There is a very simple method to show that the angle in a semi circle is equal to 90 degree.
There is a theorem that the angle subtended by an arc at the centre of a circle is double the angle subtended by it at any other point on the remaining part of the circle.
Here, let us say that 'O' is the centre of the circle.
Now we know that, Angle AOB = 180 degree, as AB is a line.
Hence, according to the theorem, Angle ACB = 90 degree.