Lets us consider a semicircle with diameter AB. If C is any point on the semicircle, then ABC forms a right angled triangle with right angle at C .
Let CD be the perpendicular to AB dropped from C . Let AD= a and DB=b
The trianges DAC and DCB are similar , hence
if r is the radius of the semicircle , then
If that is if the Point D comes on the center of the circle then
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