If the line `x=y=z` intersect the line `s in Adotx+s in Bdoty+s in Cdotz=2d^2,s in2Adotx+s in2Bdoty+s in2Cdotz=d^2,` then find the value of `sinA/2dotsinB/2dotsinC/2w h e r eA ,B ,C` are the angles of a triangle.

In DeltaABC if 2s =a +b+c and (s-b)(s-c)=x" sin"^(2)(A)/(2) ,then the value of x is

The lines 3x+4y=9&4x-3y+12=0 intersect at Pdot The first line intersects x-a xi s at A and the second line intersects y-a xi s at Bdot Then the circumradius of the triangle P A B is 3/2 (b) 5/2 (c) 10 (d) none

If a/(sinA)=K , then the area of "DeltaA B C" in terms of K and sines of the angles is (K^2)/4s in A\ s in B\ s in C (b) (K^2)/2s in A\ s in B\ s in C 2K^2s in A\ s in B\ "sin"(A+B) (d) none

In a scalene triangle A B C ,D is a point on the side A B such that C D^2=A D D B , sin s in A S in B=sin^2C/2 then prove that CD is internal bisector of /_Cdot

The distance between the lines x=1-4t, y=2+t, z=3+2t" and "x=1+s, y=4-2s, z=-1+s is

If a + b+ c =2s , thent the value of (s-a)^(2) + (s-b)^(2) +( s-c)^2 will be

In triangle ABC, sin((A)/(2))sin((C)/(2))=sin((B)/(2)) and '2s' is the perimeter of the triangle. Then the value of s is

Let A B C be a triangle right-angled at Aa n dS be its circumcircle. Let S_1 be the circle touching the lines A B and A C and the circle S internally. Further, let S_2 be the circle touching the lines A B and A C produced and the circle S externally. If r_1 and r_2 are the radii of the circles S_1 and S_2 , respectively, show that r_1r_2=4 area ( A B C)dot

In the shown fig. S1 and S2 are two identical coher- ent sources of sound, separated by a distance d. A receiver moves along the line XY (which is parallel to line S1 S2) to detect the intensity of sound at various points on the line. Distance of line XY from line S1 S2 is D (gt gt d) . Point O is the foot of perpendicular bisector of the line S1 S2 on XY. Distance of first intensity maxima (on line XY) measured from O is y. Find percentage change in value of y if the temperature of air increases by 1%.