SOLUTION: Prove that the inscribed angle in a semi circle is 90 degrees

Question 17635: Prove that the inscribed angle in a semi circle is 90 degrees
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
consider a circle with O as centre .take any diameter AOB.the diameter AOB divides the circle in to two equal halves called semicircles.take any point P on the circumference of the circle.join AP and PB .the angle APB,that is the angle subtended by AB at the circumference is called inscribed angle in a semicircle .There is a theorem that angle subtended or made by a chord (includes diameter too) at the centre of the circle is twice the angle subtended by the same chord at the circumference.now AB makes a straight angle of 180 at the centre O as AOB is a diameter.hence AB makes half of 180 or 90 degrees at the circumference.so angle APB the inscribed angle in a semicircle is 90 degrees
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