ABCD is a trapezium such that `A B||C Da n dC B` is perpendicular to them. If `/_A D B=theta,B C=p ,a n dC D=q` , show that `A B=((p^2+q^2)sintheta)/(pcostheta+qsintheta)`

ABCD is a trapezium such that AB and CD are parallel and B C_|_C D . If /_A D B""=theta,""B C""=""p""a n d""C D""=""q , then AB is equal to (1) (p^2+q^2costheta)/(pcostheta+qsintheta) (2) (p^2+q^2)/(p^2costheta+q^2sintheta) (3) ((p^2+q^2)sintheta)/((pcostheta+qsintheta)^2) (4) ((p^2+q^2)sintheta)/(pcostheta+qsintheta)

A B C D is a trapezium in which A B D C . P and Q are points on sides A D and B C such that P Q A B . If P D=18 , B Q=35 and Q C=15 , find A D .

If p sintheta+qcostheta=3&qsintheta-pcostheta=2 , then p^(2)+q^(2)=?

In Figure, line l is the bisector of angle A a n d B is any point on ldotB P a n d B Q are perpendiculars from B to the arms of Adot Show that: A P B ~= A Q B BP=BQ or B is equidistant from the arms of /_A

In Figure, A N and C P are perpendicular to the diagonal B D of a parallelogram A B C Ddot Prove that : A D N~= C B P (ii) A N=C P

A B C D is a cyclic quadrilateral whose diagonals A Ca n dB D intersect at P . If A B=D C , Prove that : P A B~= P D C P A=P Da n dP C=P B A D B C

line l is the bisector of an angle /_A\ a n d/_B is any point on l. BP and BQ are perpendiculars from B to the arms of /_A . Show that: (i) DeltaA P B~=DeltaA Q B (ii) BP = BQ or B is equidistant from the arms of /_A

In Fig. 4.230, each of P A ,\ Q B ,\ R C and S D is perpendicular to l . If A B=6c m , B C=9c m , C D=12 c m and P S=36 c m , then determine P Q ,\ Q R and R S . (FIGURE)