`A B C D` is a quadrilateral such that `/_D=90^circ` A circle `C(O , r)` touches the sides `A B ,B C ,C D` and `D A` at `P ,Q, R` and `S` respectively. If `B C=38 c m ,C D=25 c m` and `B P=27 c m ,` find `rdot`

In Figure, a quadrilateral A B C D is drawn to circumscribe a circle such that its sides A B ,\ B C ,\ C D and A D touch the circle at P ,\ Q ,\ R and S respectively. If A B=x\ c m , B C=7c m , C R=3c m and A S=5c m , then x= (a) 10 (b) 9 (c) 8 (d) 7

In Figure, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches sides BC, AB, AD and C D at points P, Q, R and S respectively. If A B=29c m ,A D=23 c m ,/_B=90^0 and D S=5c m , then the radius of the circle (in cm) is (a) 11 (b) 18 (c) 6 (d) 15

In A B C , the bisector of /_A intersects B C in D . If A B=18 c m , A C=15 c m and B C=22 c m , find B D

In a A B C , D and E are points on the sides A B and A C respectively such that D E || B C If A D=6\ c m , D B=9\ c m and A E=8\ c m , find A C .

In Figure, the incircle of A B C touches the sides B C ,\ C A and A B\ a t\ D ,\ E and F respectively. Show that A F+B D+C E=A E+B F+C D=1/2(P e r i m e t e r\ of\ A B C) .

In A B C , P and Q are points on sides A B and A C respectively such that P Q ||B C . If A P=3c m , P B=5c m and A C=8c m , find A Q .

In a A B C , D and E are points on the sides A B and A C respectively such that D E// B C If A D=2\ c m , A B=6\ c m and A C=9\ c m , find A E . .

M ,\ N\ a n d\ P are the mid-points of A B ,\ A C\ a n d\ B C respectively. If M N=3c m ,\ N P=3. 5 c m\ a n d\ M P=2. 5 c m , calculate B C ,\ A B\ a n d\ A C

In a triangle, P ,\ Q\ a n d\ R are the mid-points of sides B C ,\ C A\ a n d\ A B respectively. If A C=21\ c m ,\ B C=29 c m\ a n d\ A B=30 c m , find the perimeter of the quadrilateral A R P Q

In square A B C D ,\ P\ a n d\ Q are mid-point of A B\ a n d\ C D respectively. If A B=8c m\ a n d\ P Q\ a n d\ B D intersect at O , then find area of O P B