Let `S` be a square of nit area. Consider any quadrilateral, which has none vertex on each side of `Sdot` If `a ,b ,ca n dd` denote the lengths of the sides of het quadrilateral, prove that `2lt=a^2+b^2+c^2+x^2lt=4.`

Let alt=blt=c be the lengths of the sides of a triangle. If a^2+b^2 < c^2, then prove that triangle is obtuse angled .

The two adjacent sides of a cyclic quadrilateral are 2a n d5 and the angle between them is 60^0dot If the area of the quadrilateral is 4sqrt(3) , find the remaining two sides.

In Delta ABC , if r_(1) lt r_(2) lt r_(3) , then find the order of lengths of the sides

Let a , ba n dc be the three sides of a triangle, then prove that the equation b^2x^2+(b^2=c^2-alpha^2)x+c^2=0 has imaginary roots.

An equilateral triangle is inscribed in an ellipse whose equation is x^2+4y^2=4 If one vertex of the triangle is (0,1) then the length of each side is

If the sides a , b and c of ABC are in AdotPdot, prove that acos^2(C/2)+c cos^2(A/2)=(3b)/2

If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the sides opposite to A, B and C respectively, then the value of the expression (a)/(c) sin 2C + (c)/(a) sin 2A is

lf a quadrilateral is formed by four tangents to the ellipse x^2/9+y^2/4=1 then the area of the square is equal to

Consider a DeltaABC in which the sides are a = (n +1), b = (n + 2), c = n with tan C = 4//3 , then the value of Delta is _____

If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in G.P., then prove that a^2, b^2,c^2 are in A.P.