Question

ps
inte
A
bet
O
(C) 70°
(d) 80°
(1) In the figure XY and X'y' are two parallel tangents
to a circle with centre 0 and another tangent AB
with point of contact C intersecting XY at A and
x'y' at B then ZAOB =
(a) 80°
(b) 100°
(C) 90°
(d) 60°
В​

Answer 1

Answer:

and the correct answer is option b

Answer 2

Answer:

• Qᴜᴇꜱᴛɪᴏɴ:

ɪɴ ꜰɪɢ., xʏ ᴀɴᴅ x'ʏ' ᴀʀᴇ ᴛᴡᴏ ᴘᴀʀᴀʟʟᴇʟ ᴛᴀɴɢᴇɴᴛꜱ ᴛᴏ ᴀ ᴄɪʀᴄʟᴇ ᴡɪᴛʜ ᴄᴇɴᴛʀᴇ ᴏ ᴀɴᴅ ᴀɴᴏᴛʜᴇʀ ᴛᴀɴɢᴇɴᴛ ᴀʙ ᴛᴏᴜᴄʜɪɴɢ ᴀᴛ ᴄ, ɪɴᴛᴇʀꜱᴇᴄᴛɪɴɢ xʏ ᴀᴛ ᴀ ᴀɴᴅ x'ʏ' ᴀᴛ ʙ. ᴘʀᴏᴠᴇ ᴛʜᴀᴛ ᴢᴀᴏʙ = 90°.

• ꜱᴏʟᴜᴛɪᴏɴ :

ʟᴇᴛ ᴜꜱ ᴊᴏɪɴ ᴘᴏɪɴᴛ ᴏ ᴛᴏ ᴄ.

ɪɴ ᴀᴏᴘᴀ ᴀɴᴅ ᴀᴏᴄᴀ,

ᴏᴘ = ᴏᴄ (ʀᴀᴅɪɪ ᴏꜰ ᴛʜᴇ ꜱᴀᴍᴇ ᴄɪʀᴄʟᴇ)

ᴀᴘ = ᴀᴄ (ᴛᴀɴɢᴇɴᴛꜱ ꜰʀᴏᴍ ᴘᴏɪɴᴛ ᴀ)

ᴀᴏ = ᴀᴏ (ᴄᴏᴍᴍᴏɴ ꜱɪᴅᴇ)

ᴀᴏᴘᴀ = ᴀᴏᴄᴀ (ꜱꜱꜱ ᴄᴏɴɢʀᴜᴇɴᴄᴇ ᴄʀɪᴛᴇʀɪᴏɴ)

ᴛʜᴇʀᴇꜰᴏʀᴇ, ᴘ ᴄ, ᴀ + ᴀ, ᴏ - ᴏ

ᴢᴘᴏᴀ = ᴢᴄᴏᴀ ... (1)

ꜱɪᴍɪʟᴀʀʟʏ, ᴀᴏQʙ = ᴀᴏᴄʙ

ᴢQᴏʙ = 2ᴄᴏʙ . (ɪɪ) ...

ꜱɪɴᴄᴇ ᴘᴏQ ɪꜱ ᴀ ᴅɪᴀᴍᴇᴛᴇʀ ᴏꜰ ᴛʜᴇ ᴄɪʀᴄʟᴇ, ɪᴛ ɪꜱ ᴀ ꜱᴛʀᴀɪɢʜᴛ ʟɪɴᴇ.

ᴛʜᴇʀᴇꜰᴏʀᴇ, ᴘᴏᴀ + 2ᴄᴏᴀ + ᴄᴏʙ + ᴢQᴏʙ = 180°

ꜰʀᴏᴍ ᴇQᴜᴀᴛɪᴏɴꜱ (ɪ) ᴀɴᴅ (ɪɪ), ɪᴛ ᴄᴀɴ ʙᴇ ᴏʙꜱᴇʀᴠᴇᴅ ᴛʜᴀᴛ

2∠ᴄᴏᴀ+2∠ᴄᴏʙ=180∘

∠ᴄᴏᴀ+∠ᴄᴏʙ=90∘

∠ᴀᴏʙ=90∘