CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

A circle is inscribed in an equilateral triangle of side a, the area of any square inscribed in the circle is



Solution

The correct option is C


If p be the altitude, then p = asin 60 = a23.

Since the triangle is equilateral, therefore centroid, orthocentre, circumcentre and incentre all coincide.

Hence, radius of the inscribed circle = 13p=a23=r or diameter=2r=a3.

Now if x be the side of the square inscribed, then angle in a semicircle being a right angle, hence

x2+x2=d2=4r22x2=a23

So the area of the square is x2=a26

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More


People also searched for
View More



footer-image