Math, asked by adityachoudhary2956, 9 months ago

❣❣❣❣❣❣✧༺♥༻✧❣❣❣❣❣❣❣❣
In Fig. 6.54, 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❣❣❣❣❣❣❣
❣❣»»——⍟——««❣»»——⍟——««❣❣

.

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Answers

Answered by surendrasahoo

Hello Aditya.

Your answer is in the given attachment

It may help you.....

#thank you#

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Answered by XxMissPaglixX

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ʜᴇʟʟᴏ ᴅᴇᴀʀ,

ɢɪᴠᴇɴ ᴛʜᴀᴛ:-

∆ ᴏʙᴄ ᴀɴᴅ ᴏ ɪs ᴀ ᴘᴏɪɴᴛ ɪɴ ᴛʜᴇ ᴇɴᴛᴇʀɪᴏʀ ᴏғ ᴛʜᴇ ∆ᴀʙᴄ

ᴏᴄ⊥ʙᴄ , ᴏᴇ⊥ᴀᴄ , ᴀɴᴅ ᴏғ⊥ᴏʙ

ᴄᴏɴsᴛʀᴜᴄᴛɪᴏɴ :- ɴᴏᴡ ᴊᴏɪɴ ᴛʜᴇ ᴘᴏɪɴᴛ ᴏ ғʀᴏᴍ ʙ,ᴄ,ᴀɴᴅᴀ

ɪɴ ∆ᴏᴀғ ,<ғ=90°

ᴏᴀ²= ᴀғ²+ᴏғ²---------(1)

ɪɴ ∆ᴏᴇᴄ , <ᴇ=90°

ᴏᴄ²=ᴏᴇ²+ᴇᴄ²--------------(2)

ɪɴ ᴀɴᴏᴛʜᴇʀ , ∆ᴏʙᴅ, <ᴅ=90°

ᴏʙ²=ᴏᴅ²+ʙᴅ²-----------(3)

ɴᴏᴡ ᴀᴅᴅɪɴɢ---(1) ,---(2),,ᴀɴᴅ --(3)

ᴡᴇ ɢᴇᴛ,

ᴏᴀ²+ᴏᴄ²+ᴏʙ²=ᴀғ²+ᴏғ²+ᴏᴇ²+ᴇᴄ²+ᴏᴅ²+ʙᴅ²

=> ᴏᴀ²+ᴏʙ²+ᴏᴄ²-ᴏᴅ²-ᴏᴇ²-ᴏғ²=ᴀғ²+ʙᴅ²+ᴄᴇ²

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