Properties of T...

In a ∆PQR, P is the largest angle and cos P = 1/3, Further in circle of the triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even integers, Then, possible length(s) of the side (s) of the triangle is (are)

The area of a circle and the area of a regular polygon of n sides of the perimeter equal to that of that circle are in the ratio

If A, A₁, A₂ and A₃ and the areas of the incricle and excricles, then 1/√A₁ + 1/√A₂ + 1/√A₃ is equal to

In a triangle, if r₁ = 2r₂ = 3r₃, then a/b + b/c + c/a is equal to

In a ∆ABC, a : b : c = 4 : 5 : 6. The ratio of the radius of the circumcircle to that of the incircle is

In radius of a circle which is inscribed in an isosceles triangle one of whose angle is 2π/ 3 , is √3, then area of triangle is

The circumradius of the triangle whose sides are 13, 12 and 5 is

If p₁, p₂, p₃ are respectively the perpendiculars from the vertices of a triangle to the opposite side, then p₁, p₂, p₃ is equal to

In a ∆ABC, let ∠C = π/2, if r is the inradius and R is the circumraidus of the ∆ABC, then 2 (r + R) equals