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Shade : (1)/(3) of the rectangles in box...

Shade : `(1)/(3)` of the rectangles in box (a)
(ii) `(2)/(3)` of the circles in box (b)
(iii) `(1)/(2)` of the triangles in box (c )

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Shade: 1/2 of the circles in box

Shade: 2/3 of the traingles in box

Shade: 3/5 of the squares in box.

The circle inscribed in the triangle ABC touches the side BC, CA and AB in the point A_(1)B_(1) and C_(1) respectively. Similarly the circle inscribed in the Delta A_(1) B_(1) C_(1) touches the sieds in A_(2), B_(2), C_(2) respectively and so on. If A_(n) B_(n) C_(n) be the nth Delta so formed, prove that its angle are pi/3-(2)^-n(A-(pi)/(3)), pi/3-(2)^-n(B-(pi)/(3)),pi/3-(2)^-n(C-(pi)/(3)). Hence prove that the triangle so formed is ultimately equilateral.

Prove that the points A (1,2,3), B(2,3,1) and C(3,1,2) are the vertices of an equilateral triangle.

Fill in the boxes. square - 1/5 = 1/2