Math, asked by creamiepie, 1 year ago

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ᴛʜᴇ ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ ғʀᴏᴍ 'ᴀ' ᴏɴ ᴛʜᴇ sɪᴅᴇ ʙᴄ ᴏғ  ∆ᴀʙᴄ ɪɴᴛᴇʀsᴇᴄᴛs ʙᴄ ᴀᴛ ᴅ sᴜᴄʜ ᴛʜᴀᴛ ʙᴅ:ᴄᴅ = 3:2. ᴘʀᴏᴠᴇ ᴛʜᴀᴛ 

 {AB}^{2}  -  {AC}^{2}  =  \frac{1}{5} \:  {BC}^{2}
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Answers

Answered by Anonymous
5
let BD =3x

DC = 2x

in ABD.

AD^2 = AB^2 - BD^2 = AB^2 - 9x^2

In ADC

AD^2 = AC^2 - DC^2 = AC^2 - 4 X^2

COMPARE

AB^2 - 9x^2 = AC^2 - 4x^2

AB^2 - AC^2 = -4x^2 + 9x^2 = 5x^2

BC= 3x+ 2x = 5x

BC^2 = 25 x^2

1/5 . BC^2 = 5x^2

So AB^2 - AC^2 = 1/5. BC^2
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Answered by RvChaudharY50
25

See solution in image .....

\huge\underline\mathfrak\green{Hope\:it\:Helps\:You}

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