State True or False.
In the given figure, O is a point in the interior of a triangle ABC, OD ⊥ BC, OE ⊥AC and OF ⊥AB. Then $AF 2 + BD 2 + CE 2 = O A 2 + O B 2 + O C 2 − O F 2 − O D 2 − O E 2$ .

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given figure is,
Question Image

We know that Pythagoras theorem states, in a right-angled triangle,

(h y p o t e n u s e) 2 = (b a s e) 2 + (p e r p e n d i c u l a r) 2

.
Using Pythagoras theorem in right-angled

Δ AFO, Δ E O C, Δ B D O

O A 2 = A F 2 + O F 2 ⇒ A F 2 = O A 2 − O F 2 ......... (1)

O B 2 = B D 2 + O D 2 ⇒ B D 2 = O B 2 − O D 2 ........... (2)

O C 2 = C E 2 + O E 2 ⇒ C E 2 = O C 2 − O E 2 ........... (3)

Adding (1), (2) and (3),

⇒ A F 2 + B D 2 + C E 2 = O A 2 − O F 2 + O B 2 − O D 2 + O C 2 − O E 2

⇒ A F 2 + B D 2 + C E 2 = O A 2 + O B 2 + O C 2 − O F 2 − O D 2 − O E 2

The statement is the same as the answer obtained, hence the statement is true.
Hence the correct option is 1.

Watch 3-min video & get full concept clarity