Question

AB and BC are two congruent chords of a circle with centre O.OP perpendicular to AB and OD perpendicular to BC.
show that angleABO = angleOBO.​

Answer 1

Answer:

 ✒ ɢɪᴠᴇɴ:-

⛄ ᴀʙ ᴀɴᴅ ᴄᴅ ᴀʀᴇ ᴛᴡᴏ ᴄʜᴏʀᴅs ᴏғ ᴀ ᴄɪʀᴄʟᴇ ᴡɪᴛʜ ᴄᴇɴᴛʀᴇ ᴏ.

⛄ ᴍᴘ=ɴᴘ.

⛄ "ᴏᴍ" ɪs ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ ᴛᴏ "ᴀʙ" ᴀɴᴅ "ᴏɴ" ɪs ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ ᴛᴏ "ᴅᴄ".

✒ ᴛᴏ ᴘʀᴏᴠᴇ:-

⛄ᴀʙ = ᴄᴅ.

✒ ᴘʀᴏᴏғ:-

⛄ ᴄᴏɴsɪᴅᴇʀ ∆ᴏᴍᴘ ᴀɴᴅ ∆ᴏɴᴘ. ʜᴇʀᴇ,

↪ᴀɴɢʟᴇ ᴏᴍᴘ = ᴀɴɢʟᴇ ᴏɴᴘ = 90° [ɢɪᴠᴇɴ]

↪ᴏᴘ = ᴏᴘ [ᴄᴏᴍᴍᴏɴ]

↪ᴍᴘ = ɴᴘ [ɢɪᴠᴇɴ]

ᴛʜᴇʀᴇғᴏʀᴇ,

∆ᴏᴍᴘ ≈ ∆ᴏɴᴘ [ʙʏ ʀʜs ʀᴜʟᴇ]

=) ᴏᴍ = ᴏɴ [ʙʏ ᴄᴘᴄᴛ]

=) ᴀʙ = ᴄᴅ

[sɪɴᴄᴇ ᴄʜᴏʀᴅs ᴇϙᴜɪᴅɪsᴛᴀɴᴛ ғʀᴏᴍ ᴛʜᴇ ᴄᴇɴᴛʀᴇ ᴀʀᴇ ᴇϙᴜᴀʟ]

Ⓗⓔⓝⓒⓔ Ⓟⓡⓞⓥⓔⓓ!!

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