CameraIcon

SearchIcon

MyQuestionIcon

179

You visited us 179 times! Enjoying our articles? Unlock Full Access!

Distances between Special Points in a Triangle

In the figure...

Question

In the figure, diagonals $A C$ and $B D$ of a quadrilateral $A B C D$ intersect at $O$ such that $O B = O D$ , show that $a r (Δ D O C) = a r (Δ A O B)$

Open in App

Solution

$B O = O D$
Since $B O = O D$ is the mid point
we know thta $a$ mid point of a $△$ divides it into two $△$ of equal areas
$C O$ is medpoint of $△ B C D$
i.e., $a r (△ C O D) = a r (△ C O B) - - - (1)$
$A O$ is a medpoint of $△ A B D$
i.e. $a r (△ A O D) = a r (△ A O B) - - - (2)$
from $(I)$ & $(I I)$ we have
$a r (△ C O D) + a r (△ A O D) = a r (△ C O B) + a r (△ A O B)$
$a r (△ A D C) = a r (△ A B C)$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Question 6 (ii)
In the given figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that:
(ii) ar(DCB) = ar(ACB)

Q. Question 6 (ii)
In the given figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that:
(ii) ar(DCB) = ar(ACB)

Q. In the figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB=OD. If AB=CD, then show that
1. ar(DOC)=ar(AOB)
2. ar(DCB)=ar(ACB)
3. DA||CD or ABCD is a parallelogram.

Q. Question 6 (i)
In the given figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that:
(i) ar(DOC) = ar(AOB)

Q. In the given figure diagonals AC and BD the of quadrilateral ABCD intersect at O such that OB =OD.
If AB =CD, then show that:
(i) ar (DOC) =ar (AOB)
(ii) ar (DCB) =ar (ACB)
(iii) DA||CB or ABCD is a parallelogram

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Introduction

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Distances between Special Points in a Triangle

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon