Question

in a quadrilateral ABCD.show that ab+bc+cd+da→ac+bd
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Answer 1

ᴀʙᴄᴅ ɪs ᴀ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ. ɪᴛs ᴅɪᴀɢᴏɴᴀʟs ᴀʀᴇ ᴀᴄ ᴀɴᴅ ʙᴅ.

ɪɴ ᴛʀɪᴀɴɢʟᴇ ᴀᴄʙ, ᴀʙ + ʙᴄ > ᴀᴄ - 1

ɪɴ ᴛʀɪᴀɴɢʟᴇ ʙᴅᴄ, ʙᴄ + ᴄᴅ > ʙᴅ - 2

ɪɴ ᴛʀɪᴀɴɢʟᴇ ᴀᴄᴅ, ᴀᴅ + ᴅᴄ > ᴀᴄ -3

ɪɴ ᴛʀɪᴀɴɢʟᴇ ʙᴀᴅ, ᴀʙ + ᴀᴅ > ʙᴅ -4

ᴀᴅᴅɪɴɢ 1,2,3 ᴀɴᴅ 4,

ᴀʙ + ʙᴄ + ʙᴄ + ᴄᴅ + ᴀᴅ + ᴅᴄ + ᴀʙ + ᴀᴅ > ᴀᴄ + ʙᴅ + ᴀᴄ + ʙᴅ

2ᴀʙ + 2ʙᴄ + 2ᴄᴅ + 2ᴀᴅ > 2ᴀᴄ + 2ʙᴅ

ᴀʙ + ʙᴄ + ᴄᴅ + ᴀᴅ > ᴀᴄ + ʙᴅ.