In Fig.9.29, `a r"\ "(B D P)"\ "="\ "a r"\ "(A R C)` and `a r"\ "(B D P)"\ "="\ "a r"\ "(A R C)` . Show that both the quadrilaterals ABCD and DCPR are trapeziums.

In Fig.9.28, A P" "||" "B Q" "||" "C R . Prove that a r" "(A Q C)" "=" "a r" "(P B R)dot

In Figure, A P || B Q\ || C R . Prove that a r\ ( A Q C)=\ a r\ (P B R)

Diagonals A C\ a n d\ B D of a quadrilateral A B C D intersect at O in such a way that a r\ ( A O D)=a r\ (\ B O C)dot Prove that A B C D is a trapezium.

A B C D IS A PARALLELOGRAM AND O is any point in its interior. Prove that: a r\ ( A O B)+\ a r\ ( C O D)=\ a r\ ( B O C)+\ a r( A O D) a r\ ( A O B)+a r\ (C O D)=1/2\ a r(^(gm)A B C D) Given: A parallelogram A B C D\ a n d\ O is a point in its interior. To Prove: a r\ (\ A O B)+\ a r( C O D)=a r\ ( B O C)+a r( A O D)

Diagonals A C a n d B D of a quadrilateral A B C D intersect at O in such a way that a r ( A O D)=a r ( B O C)dot Prove that A B C D is a trapezium.

The exradii r_1,r_2 and r_3 of /_\A B C are in H.P. Show that its sides a , b a n d c are in AdotPdot

The exradii r_1,r_2 and r_3 of /_\A B C are in H.P. Show that its sides a , b a n d c are in AdotPdot

The exradii r_1,r_2 and r_3 of /_\A B C are in H.P. Show that its sides a , b a n d c are in AdotPdot

If A B C D is a parallelogram, then prove that a r\ (\ A B D)=\ a r\ (\ B C D)=\ a r\ (\ A B C)=\ a r\ (\ A C D)=1/2\ a r\ (|""|^(gm)A B C D)

In Fig. 9.25, diagonals AC and BD of quadrilateral ABCD intersect at O such that O B" "=" "O D . If A B" "=" "C D , then show that: (i) a r" "(D O C)" "=" "a r" "(A O B) (ii) a r" "(D C B)" "=" "a r" "(A C B) (iii) D A" "||" "C