Question

photo dekh kr solve kro​

Answer 1

$\huge\underbrace\pink{Answer}$

Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ BCDE

Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ BCDE∠ʙ=∠ᴅ (ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)

Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ BCDE∠ʙ=∠ᴅ (ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ABCD

Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ BCDE∠ʙ=∠ᴅ (ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ABCD∠B=∠ADF (ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)

Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ BCDE∠ʙ=∠ᴅ (ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ABCD∠B=∠ADF (ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)⟹∠ᴀ+∠ʙ=∠ᴄ+∠ᴅ

Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ BCDE∠ʙ=∠ᴅ (ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ABCD∠B=∠ADF (ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)⟹∠ᴀ+∠ʙ=∠ᴄ+∠ᴅ ⟹∠ᴀ+∠ʙ=∠ᴄ+∠ʙ

Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ BCDE∠ʙ=∠ᴅ (ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ABCD∠B=∠ADF (ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)⟹∠ᴀ+∠ʙ=∠ᴄ+∠ᴅ ⟹∠ᴀ+∠ʙ=∠ᴄ+∠ʙ∠ᴀ=∠ᴄ

Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ BCDE∠ʙ=∠ᴅ (ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ABCD∠B=∠ADF (ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)⟹∠ᴀ+∠ʙ=∠ᴄ+∠ᴅ ⟹∠ᴀ+∠ʙ=∠ᴄ+∠ʙ∠ᴀ=∠ᴄᴀɴᴅ ɪᴛ ɪs ɢɪᴠᴇɴ ᴛʜᴀᴛ

Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ BCDE∠ʙ=∠ᴅ (ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ABCD∠B=∠ADF (ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)⟹∠ᴀ+∠ʙ=∠ᴄ+∠ᴅ ⟹∠ᴀ+∠ʙ=∠ᴄ+∠ʙ∠ᴀ=∠ᴄᴀɴᴅ ɪᴛ ɪs ɢɪᴠᴇɴ ᴛʜᴀᴛ∠ᴀ=∠ʙ

Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ BCDE∠ʙ=∠ᴅ (ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ABCD∠B=∠ADF (ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)⟹∠ᴀ+∠ʙ=∠ᴄ+∠ᴅ ⟹∠ᴀ+∠ʙ=∠ᴄ+∠ʙ∠ᴀ=∠ᴄᴀɴᴅ ɪᴛ ɪs ɢɪᴠᴇɴ ᴛʜᴀᴛ∠ᴀ=∠ʙsᴏ, ∠ʙ=∠ᴄ

Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ BCDE∠ʙ=∠ᴅ (ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ABCD∠B=∠ADF (ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)⟹∠ᴀ+∠ʙ=∠ᴄ+∠ᴅ ⟹∠ᴀ+∠ʙ=∠ᴄ+∠ʙ∠ᴀ=∠ᴄᴀɴᴅ ɪᴛ ɪs ɢɪᴠᴇɴ ᴛʜᴀᴛ∠ᴀ=∠ʙsᴏ, ∠ʙ=∠ᴄHᴇɴᴄᴇ ∠ᴄ=∠ᴅ

Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ BCDE∠ʙ=∠ᴅ (ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ABCD∠B=∠ADF (ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)⟹∠ᴀ+∠ʙ=∠ᴄ+∠ᴅ ⟹∠ᴀ+∠ʙ=∠ᴄ+∠ʙ∠ᴀ=∠ᴄᴀɴᴅ ɪᴛ ɪs ɢɪᴠᴇɴ ᴛʜᴀᴛ∠ᴀ=∠ʙsᴏ, ∠ʙ=∠ᴄHᴇɴᴄᴇ ∠ᴄ=∠ᴅ⟹DE ʙɪsᴇᴄᴛs ∠ADF

Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ BCDE∠ʙ=∠ᴅ (ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)Iɴ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ABCD∠B=∠ADF (ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ᴏғ ᴀ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ᴇϙᴜᴀʟ ᴛᴏ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)⟹∠ᴀ+∠ʙ=∠ᴄ+∠ᴅ ⟹∠ᴀ+∠ʙ=∠ᴄ+∠ʙ∠ᴀ=∠ᴄᴀɴᴅ ɪᴛ ɪs ɢɪᴠᴇɴ ᴛʜᴀᴛ∠ᴀ=∠ʙsᴏ, ∠ʙ=∠ᴄHᴇɴᴄᴇ ∠ᴄ=∠ᴅ⟹DE ʙɪsᴇᴄᴛs ∠ADFsᴏʟᴜᴛɪᴏɴ

Ⓗᴏᴘᴇ ɪᴛ ʜᴇʟᴘⓈ

Answer 2

In quadrilateral BCDE

∠b=∠d (exterior angle of a cyclic quadrilateral is equal to the opposite interior angle)

In quadrilateral ABCD

∠B=∠ADF (exterior angle of a cyclic quadrilateral is equal to the opposite interior angle)

⟹∠a+∠b=∠c+∠d

⟹∠a+∠b=∠c+∠b

∠a=∠c

and it is given that

∠a=∠b

so, ∠b=∠c

Hence ∠c=∠d

⟹DE bisects ∠ADF