CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Opposite & Adjacent Sides in a Right Angled Triangle

In the follow...

Question

In the following figure, O is a point in the interior of a triangle ABC, OD ⊥ BC, OE ⊥ AC and OF ⊥ AB. Show that

(i) OA² + OB² + OC² − OD² − OE² − OF² = AF² + BD² + CE²

(ii) AF² + BD² + CE²= AE² + CD² + BF²

Open in App

Solution

Join OA, OB, and OC.

(i) Applying Pythagoras theorem in ΔAOF, we obtain

Similarly, in ΔBOD,

Similarly, in ΔCOE,

(ii) From the above result,

Suggest Corrections

thumbs-up

0

Similar questions

Q. In the above figure,

O

is a point in the interior of a triangle

A B C,

O D ⊥ B C, O E ⊥ A C

O F ⊥ A B

. Show that:
(i)

O A^{2} + O B^{2} + O C^{2} - O D^{2} - O E^{2} - O F^{2} = A F^{2} + B D^{2} + C E^{2}

A F^{2} + B D^{2} + C E^{2} = A E^{2} + C D^{2} + B F^{2}

Q. In Figure, O is a point in the interior of a triangle ABC, OD

⊥

⊥

⊥

O A^{2} + O B^{2} + O C^{2} - O D^{2} - O E^{2} - O F^{2} = A F^{2} + B D^{2} + C E^{2}

.

Q. In given figure from a point O in the interior of a

△ A B C

, perpendiculars OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove that :

{A F}^{2} + {B D}^{2} + {C E}^{2} = {O A}^{2} + {O B}^{2} + {O C}^{2} - {O D}^{2} - {O E}^{2} - {O F}^{2}

{A F}^{2} + {B D}^{2} + {C E}^{2} = {A E}^{2} + {C D}^{2} + {B F}^{2}

Q. From a point O in the interior of a

Δ A B C

, perpendiculars OD, OE, & OF are drawn to the sides BC, CA & AB respectively. Prove that :
[i]

A F^{2} + B D^{2} + C E^{2} = O A^{2} + O B^{2} + O C^{2} - O D^{2} - O E^{2} - O F^{2}

A F^{2} + B D^{2} + C E^{2} = A E^{2} + C D^{2} + B F^{2}

Q. In the given fig O is a point in the interior of a triangle of a triangle

A B C, O D ⊥ B C, O E ⊥ A C

O F ⊥ A B

{O A}^{2} + {O B}^{2} + {O C}^{2} - {O D}^{2} - {O E}^{2} - {O F}^{2} = {A F}^{2} + {B D}^{2} + {C E}^{2}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Trigonometric Ratios

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Opposite & Adjacent Sides in a Right Angled Triangle

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon