If a triangle ABC, inscribed in a fixed circle, be slightly varied in such away as to have its vertices always on the circle, then show that `(d a)/(c a sA)+(d b)/(cosB)+(d c)/(cosC)=0.`

If in a triangle A B C , the side c and the angle C remain constant, while the remaining elements are changed slightly, using differentials show that (d a)/(c sA)+(d b)/(cosB)=0

A triangle A B C is inscribed in a circle with centre at O , The lines A O ,B Oa n dC O meet the opposite sides at D , E ,a n dF , respectively. Prove that 1/(A D)+1/(B E)+1/(C F)=(acosA+bcosB+ccosC)/triangle

In an acute triangle A B C if sides a , b are constants and the base angles Aa n dB vary, then show that (d A)/(sqrt(a^2-b^2sin^2A))=(d B)/(sqrt(b^2-a^2sin^2B))

If ABC is an equilateral triangle inscribed in a circle and P be any point on the minor arc BC which does not coincide with B or C, prove that PA is angle bisector of angleBPC.

If A, B, C are angles of triangle ABC and a, b, c are lengths of the sides opposite to A, B, C respectively, then show that : a (sin B - sin C)+ b (sin C- sin A)+c (sin A -sin B)= 0 .

In any triangle ABC, prove that : (cosA)/a+ (cosB)/b+(cosC)/c= (a^2+b^2+c^2)/(2abc) .

A,B and C are three points on a circle with centre AO such that angleBOC = 30^@, angleAOB = 60^@ . If D is a point on the circle other than the are ABC, find angleADC

If vec a , vec b , vec c are three non-coplanar vectors and vec d* vec a = vec d* vec b= vec d* vec c= 0 then show that vec d is zero vector.

In the given figure, A,B and C are three points on a circle with centre O such that angle BOC = 30^@ and angle AOB = 60^@ . If D is a point on the circle other than the arc ABC, find angle ADC .

Find the coordinates of the vertices of a square inscribed in the triangle with vertices A(0,0),B(3,0) a n d C(2,1); given that two of its vertices are on the side A Bdot