Let `A B C D` be a quadrilateral with area `18` , side `A B` parallel to the side `C D ,a n dA B=2C D` . Let `A D` be perpendicular to `A Ba n dC D` . If a circle is drawn inside the quadrilateral `A B C D` touching all the sides, then its radius is `a = 3` (b) 2 (c) `3/2` (d) 1

A circle is inscribed in a triangle A B C touching the side A B at D such that A D=5,B D=3,if/_A=60^0 then length B C equals. (a) 4 (b) (120)/(13) (c) 13 (d) 12

Find the area of the quadrilateral A B C D having vertices A(1,1),B(7,-3),C(12 ,2), and D(7, 21) .

Let A B C be a triangle with incenter I and inradius rdot Let D ,E ,a n dF be the feet of the perpendiculars from I to the sides B C ,C A ,a n dA B , respectively. If r_1,r_2a n dr_3 are the radii of circles inscribed in the quadrilaterals A F I E ,B D I F ,a n dC E I D , respectively, prove that (r_1)/(r-1_1)+(r_2)/(r-r_2)+(r_3)/(r-r_3)=(r_1r_2r_3)/((r-r_1)(r-r_2)(r-r_3))

Let A B C be a triangle with A B=A Cdot If D is the midpoint of B C ,E is the foot of the perpendicular drawn from D to A C ,a n dF is the midpoint of D E , then prove that A F is perpendicular to B Edot

A B C is a triangle with /_B greater than /_C ,Da n dE are points on B C such that A D is perpendicular to B Ca n dA E is the bisector of angle Adot Complete the relation /_D A E=1/2()+/_C]dot

If a , ba n dc are the side of a triangle, then the minimum value of (2a)/(b+c-a)+(2b)/(c+a-b)+(2c)/(a+b-c)i s (a) 3 (b) 9 (c) 6 (d) 1

If D is the mid-point of the side B C of triangle A B C and A D is perpendicular to A C , then 3b^2=a^2-c ^2 (b) 3a^2=b^2 3c^2 b^2=a^2-c^2 (d) a^2+b^2=5c^2

Let D be the middle point of the side B C of a triangle A B Cdot If the triangle A D C is equilateral, then a^2: b^2: c^2 is equal to 1:4:3 (b) 4:1:3 (c) 4:3:1 (d) 3:4:1

If the vectors vec a , vec b ,a n d vec c form the sides B C ,C Aa n dA B , respectively, of triangle A B C ,t h e n

If sides of triangle A B C are a , ba n dc such that 2b=a+c then b/c >2/3 (b) b/c >1/3 b/c<2 (d) b/c<3/2