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.

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 ABC be a triangle with /_A=45^0dot Let P be a point on side BC with PB=3 and PC=5. If O is circumcenter of triangle ABC, then length OP is sqrt(18) (b) sqrt(17) (c) sqrt(19) (d) sqrt(15)

In a Delta ABC, AB = 52, BC = 56, CA = 60 . Let D be the foot of the altitude from A and E be the intersection of the internal angle bisector of /_BAC with BC. Find the length DE.

If an a triangle A B C , b=3 c, a n d C-B=90^0, then find the value of tanB

In triangle ABC, angle ABC =90^@ and BD bot Ac , if AB = 5 cm, BC = 12 cm, then find the length of BD.

Let A B C be a triangle. Let A be the point (1,2),y=x be the perpendicular bisector of A B , and x-2y+1=0 be the angle bisector of /_C . If the equation of B C is given by a x+b y-5=0 , then the value of a+b is (a) 1 (b) 2 (c) 3 (d) 4

Consider a triangle A B C and let a , ba n dc denote the lengths of the sides opposite to vertices A , B ,a n dC , respectively. Suppose a=6,b=10 , and the area of triangle is 15sqrt(3)dot If /_A C B is obtuse and if r denotes the radius of the incircle of the triangle, then the value of r^2 is

Let G be the centroid of triangle ABC and the circumcircle of triangle AGC touches the side AB at A If BC = 6, AC = 8 , then the length of side AB is equal to

If an a triangle A B C , a=3b and B-A=90^0, then find the value of tanA

In a right-angled triangle ABC, /_ABC =90^(@), AB= 3cm, BC= 4cm and the perpendicular BD on the side AC from the point B which meets the side AC at the point D. Determine the length of BD.