Question

11) Prove that “the angles in a semicircle is right angle”. in circle​

Answer 1

Answer:

Now POQ is a straight line passing through center O.

∴ Angle subtended by arc PQ at O is

∠POQ=180°

The angle subtended by an arc at the center is double the angle subtended by it any point on the remaining part of the circle.

∴∠POQ=2∠PAQ

2/∠POQ =∠PAQ

2/180=∠PAQ

∠PAQ=90

Hence proved.

hope this helps!!!

Answer 2

Answer:

consider a circle with diameter AB subtending an angle APB in the segment i.e the semicircle.                                                            now,   angle AOB = 180 degree.

also, angle APB = 1/2 of angle AOB    (the angle subtended by an arc at the centre is double the angle subtended by it at any                                                                        

 (point on the remaining part of the circle)

angle APB = 1/2 * 180 degree.

angle APB = 90 degree... 

therefore the angle in a semicircle is 90 degree..

hope it helped :)