Perpendiculars are drawn from the angles `A, B and C` of an acute-angled triangle onthe opposite sides, and produced to meet the circumscribing circle. If these produced parts are `alpha., beta, gamma,` respectively, then show that, then show that `a/alpha+b/beta+c/gamma=2(tanA+tanB+tanC).`

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

The lengths of the tangents drawn from the vertices A, B and C to the incicle of DeltaABC are 5, 3 and 2, respectively. If the lengths of the parts of tangents within the triangle which are drawn parallel to the sides BC, CA and AB of the triangle to the incircle are alpha, beta and gamm , respectively, then the value of [alpha + beta + gamma] (where [.] respresents the greatest integer functin) is _____

A line makes angles alpha,beta,gammaa n ddelta with the diagonals of a cube. Show that cos^2alpha+cos^2beta+cos^2gamma+cos^2delta=4//3.

If the distances of the vertices of a triangle =ABC from the points of contacts of the incercle with sides are alpha,betaa n dgamma then prove that r^2=(alphabetagamma)/(alpha+beta+gamma)

A circle of area 20 sq. units is centered at the point O. Suppose DeltaABC is inscribed in that circle and has area 8 sq. units. The central angles alpha, beta and gamma are as shown in the figure. The value of (sin alpha+sin beta+sin gamma) is equal to

In A B C , the bisector of the angle A meets the side BC at D andthe circumscribed circle at E. Prove that D E=(a^2secA/2)/(2(b+c))

If one side of a triangle is double the other, and the angles on opposite sides differ by 60^0, then the triangle is equilateral (b) obtuse angled (c) right angled (d) acute angled

If angle C of triangle ABC is 90^0, then prove that tanA+tanB=(c^2)/(a b) (where, a , b , c , are sides opposite to angles A , B , C , respectively).

Let alpha, beta, gamma be the measures of angle such that sin alpha+sin beta+sin gamma ge 2 . Then the possible value of cos alpha + cos beta+cos gamma is