Given an isosceles triangle with lateral side of length b, base angle `alphalt pi/4, R,r` the radii and O, I the centres of the circumcircle and incircle respectively, then prove that: `r= (b sin 2alpha)/(2(1+cosalopha))`

Given an isosceles triangle with lateral side of length b, base angle alphalt pi/4, R,r the radii and O, I the centres of the circumcircle and incircle respectively, then prove that: OI= |(bcos, (3alpha)/2)/(2sinalpha cos, alpha/2)|

Given an isoceles triangle with equal side of length b and angle alpha lt pi//4 , then the inradius r is given by

Given an isoceles triangle with equal side of length b and angle alpha lt pi//4 , then the circumradius R is given by

Given an isoceles triangle with equal side of length b and angle alpha lt pi//4 , then the distance between circumcenter O and incenter I is

If in an isosceles triangle with base 'a', vertical angle 20^@ and lateral side each of length 'b' is given then value of a^3+b^3 equals

A B C is an equilateral triangle of side 4c mdot If R ,r and h are the circumradius, inradius, and altitude, respectively, then (R+r)/h is equal to

A B C is an equilateral triangle of side 4c mdot If R , r, a n d,h are the circumradius, inradius, and altitude, respectively, then (R+r)/h is equal to (a) 4 (b) 2 (c) 1 (d) 3

In A B C , the three bisectors of the angle A, B and C are extended to intersect the circumcircle at D,E and F respectively. Prove that A DcosA/2+B EcosB/2+C FcosC/2=2R(sinA+sinB+sinC)

Let ABC be an isosceles triangle with base BC. If r is the radius of the circle inscribsed in DeltaABC and r_(1) is the radius of the circle ecribed opposite to the angle A, then the product r_(1) r can be equal to (where R is the radius of the circumcircle of DeltaABC )

In an acute angled triangle A B C , a semicircle with radius r_a is constructed with its base on BC and tangent to the other two sides. r_b a n dr_c are defined similarly. If r is the radius of the incircle of triangle ABC then prove that 2/r=1/(r_a)+1/(r_b)+1/(r_c)dot