Given a right triangle with `/_A =90^@`. Let M be the mid-point of BC. If the radii 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 a triangle ABC, angleC=90^@, r and R are the inradius and circumradius of the triangle ABC respectively, then 2(r+R) is equal to

Let p,q,r be the altitudes of a triangle with area s and perimeter 2t. Then the value of 1/p+1/q+1/r is

In a right -angled triangle, prove that r+2R=S.

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

In a triangle ABC, angleC=90^(@) , r and R are the in-radius and circum-radius of the triangle ABC respectively, then 2(r+R) is eqaul to

In triangle ABC, a=5,b=4,c=3. G is the centroid of triangle. If R_1 be the circumradius of triangle GAB, then the value of 325/R_1^2 must be

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 )