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`.

In triangle ABC, if r_(1)+r_(2)=3R and r_(2)+r_(3)=2R , then

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

Let ABC be a triangle and O be its orthocentre .If R and R_(1) are the circum-radii of triangle ABC and AOB , then

In a triangle ABC , if 2R + r = r_(1) , then

In a triangle ABC, if r_1 + r_3 + r = r_2 , then find the value of (sec^2 A + csc^2 B-cot^2 C) ,

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

In a right angles triangle, prove that r+2R=s.

The length of the common chord of two circles of radii r_1 and r_2 which intersect at right angles is

Find the area of the triangle P Q R with Q(3,\ 2) and the mid-points of the sides through Q being (2,\ -1) and (1,\ 2) .

A B C is a triangle in which D is the mid-point of BC and E is the mid-point of A D . Prove that area of triangle B E D=1/4area \ of triangle A B C . GIVEN : A triangle A B C ,D is the mid-point of B C and E is the mid-point of the median A D . TO PROVE : a r( triangle B E D)=1/4a r(triangle A B C)dot