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Prove that an angle inscribed in a semi-circle is a right angle.

Prove that an angle inscribed in a semi-circle is a right angle.

Grade:12th pass

1 Answers

Kaneez Fatima
13 Points
6 years ago
Consider a circle with center O, and draw a diameter AB 
Now, we have to prove that the intersectio point of lines drawn from the two diameteric ends meeting at the circumference subtends a right angle. 
Suppose they meet on the circumference at point P
Diameter will subtend an angle of 180 degrees at the center.
The angle subtended at the center is equal to half of the angle subtended at any point on the circumference hence the angle subtended at P = 1/2 × 180 = 90
Hence, proved
 

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