Given a right triangle with `/_A =90^@`. Let M be the mid-point of BC. If the inradii of the triangle `ABM and ACM` are `r_1 and r_2` then find the range of `r_1/r_2`

Let A B C be a triangle with /_B=90^0 . Let AD be the bisector of /_A with D on BC. Suppose AC=6cm and the area of the triangle ADC is 10c m^2dot Find the length of BD.

If the sides of a triangle are in the ratio 3 : 7 : 8 , then find R : r

In triangle ABC, r=(R )/(6) and r_(1)=7r . Then the measure of angle A =

in a triangle ABC , let angle C = (pi)/(2) if r the in radius and R is the circumradius of the triangle ABC , then 2( r+R) equals

If in a triangle ABC, r_(1)+r_(2)+r_(3)=9r , then the triangle is necessarily

In triangle ABC, if r_(1) = 2r_(2) = 3r_(3) , then a : b is equal to

ABC is a right triangle , right angled at A and D is the mid point of AB . Prove that BC^(2) =CD^2 +3BD^(2) .

The radii r_1, r_2,r_3 of the escribed circles of the triangle A B C are in H.P. If the area of the triangle is 24 c m^2a n d its perimeter is 24cm, then the length of its largest side is 10 (b) 9 (c) 8 (d) none of these

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 )

If R_1 is the circumradius of the pedal triangle of a given triangle A B C ,a n dR_2 is the circumradius of the pedal triangle of the pedal triangle formed, and so on R_3,R_4 then the value of sum_(i=1)^ooR_i , where R (circumradius) of A B C is 5 is 8 (b) 10 (c) 12 (d) 15