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)/(cosA)+(d b)/(cosB)=0

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 any triangle ABC, a=18,b=24,c=30 cosA,cosB,cosC

If D ,Ea n dF are three points on the sides B C ,C Aa n dA B , respectively, of a triangle A B C such that AD,BE and CF are concurrent, then show that (B D)/(C D),(C E)/(A E),(A F)/(B F)=-1

If a lt b lt c lt d then show that (x-a)(x-c)+3(x-b)(x-d)=0 has real and distinct roots.

For any triangle ABC, prove that : a(cosC-cosB)=2(b-c)cos^(2)""(A)/(2)

O ' is the centre of the inscribed circle in a 30^@ - 60^@ -90^@ DeltaABC with right angled at C. If the circle is tangent to AB at D then the angle /_COD is

Obtain the area of equilateral triangle inscribed in circle x^(2) + y^(2) + 2gx + 2fy + c = 0 .

A,B,C and D have position vectors a,b,c and d, respectively, such that a-b=2(d-c). Then,

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 are ABC, find angle ADC.