Question

Prove that the perpendicular bisector of the side of a cyclic quadrilateral are congruent

Answer 1

Answer:

Let OL, OM, ON and OP be the perpendicular bisectors of sides AB, BC, CD and AD respectively. Recall that perpendicular bisector of a line segment passes through the centre of the circle. Hence OL, OM, ON and OP pass through the centre. ... Thus the perpendicular bisectors of sides of cyclic quadrilateral are concurrent.

Answer 2

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ʟᴇᴛ ᴏʟ, ᴏᴍ, ᴏɴ ᴀɴᴅ ᴏᴘ ʙᴇ ᴛʜᴇ ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ ʙɪsᴇᴄᴛᴏʀs ᴏғ sɪᴅᴇs ᴀʙ, ʙᴄ, ᴄᴅ ᴀɴᴅ ᴀᴅ ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ. ʀᴇᴄᴀʟʟ ᴛʜᴀᴛ ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ ʙɪsᴇᴄᴛᴏʀ ᴏғ ᴀ ʟɪɴᴇ sᴇɢᴍᴇɴᴛ ᴘᴀssᴇs ᴛʜʀᴏᴜɢʜ ᴛʜᴇ ᴄᴇɴᴛʀᴇ ᴏғ ᴛʜᴇ ᴄɪʀᴄʟᴇ. ʜᴇɴᴄᴇ ᴏʟ, ᴏᴍ, ᴏɴ ᴀɴᴅ ᴏᴘ ᴘᴀss ᴛʜʀᴏᴜɢʜ ᴛʜᴇ ᴄᴇɴᴛʀᴇ. ᴛʜᴜs ɪᴛ ɪs ᴘʀᴏᴠᴇɴ ᴛʜᴀᴛ ᴛʜᴇ ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ ʙɪsᴇᴄᴛᴏʀs ᴏғ sɪᴅᴇs ᴏғ ᴄʏᴄʟɪᴄ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ᴀʀᴇ ᴄᴏɴᴄᴜʀʀᴇɴᴛ.

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