Question

In the given figure, AB and CD are two parallel chords of a circle with centre O and radius 5 cm such that AB = 8cm and CD= 6 cm. If OP is perpendicular to AB & OQ is perpendicular to CD, determine the length of PQ.​

Answer 1

Answer:

hope it helps you........

Answer 2

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✒ ɢɪᴠᴇɴ:-

⛄ ᴀʙ ᴀɴᴅ ᴄᴅ ᴀʀᴇ ᴛᴡᴏ ᴘᴀʀᴀʟʟᴇʟ ᴄʜᴏʀᴅs ᴏғ ᴀ ᴄɪʀᴄʟᴇ ᴡɪᴛʜ ᴄᴇɴᴛʀᴇ ᴏ ᴀɴᴅ ʀᴀᴅɪᴜs 5 ᴄᴍ sᴜᴄʜ ᴛʜᴀᴛ ᴀʙ = 8ᴄᴍ ᴀɴᴅ ᴄᴅ = 6 ᴄᴍ.

⛄ ᴏᴘ ɪs ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ ᴛᴏ ᴀʙ ᴀɴᴅ ᴏϙ ɪs ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ ᴛᴏ ᴄᴅ.

✒ ᴛᴏ ᴅᴇᴛᴇʀᴍɪɴᴇ:-

⛄ ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏғ ᴘϙ.

✒ ᴄᴏɴsᴛʀᴜᴄᴛɪᴏɴ:-

⛄ ᴊᴏɪɴ ᴏᴀ ᴀɴᴅ ᴏᴄ.

✒ sᴏʟᴜᴛɪᴏɴ:-

⛄ [ʜᴀᴠᴇ ᴀ ɢʟɪᴍᴘsᴇ ᴀᴛ ᴛʜᴇ ᴀᴛᴛᴀᴄʜᴍᴇɴᴛ ᴀʙᴏᴠᴇ!]

↪sɪɴᴄᴇ ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀs ғʀᴏᴍ ᴛʜᴇ ᴄᴇɴᴛʀᴇ ᴏғ ᴀ ᴄɪʀᴄʟᴇ ᴛᴏ ᴛʜᴇ ᴄʜᴏʀᴅ, ʙɪsᴇᴄᴛs ᴛʜᴇ ᴄʜᴏʀᴅ.

ᴛʜᴇʀᴇғᴏʀᴇ,

ᴀᴘ = ᴘʙ = 1/2 ᴀʙ = 4ᴄᴍ.

ᴀɴᴅ

ᴄϙ = ϙᴅ = 1/2 ᴄᴅ = 3 ᴄᴍ.

ɴᴏᴡ, ᴄᴏɴsɪᴅᴇʀ ∆ᴏᴀᴘ. ʜᴇʀᴇ,

ᴏᴘ² = ᴏᴀ² - ᴀᴘ²

[ʙʏ ᴘʏᴛʜᴀɢᴏʀᴀs ᴛʜᴇᴏʀᴇᴍ]

=) ᴏᴘ² = 5² - 4²

=) ᴏᴘ² = 25 - 16

=) ᴏᴘ² = 9

=) ᴏᴘ = 3 ᴄᴍ.

ɴᴏᴡ, ɪɴ ∆ᴏᴄϙ,

ᴏϙ² = ᴏᴄ² - ᴄϙ²

[ʙʏ ᴘʏᴛʜᴀɢᴏʀᴀs ᴛʜᴇᴏʀᴇᴍ]

=) ᴏϙ² = 5² - 3²

=) ᴏϙ² = 25 - 9

=) ᴏϙ² = 16

=) ᴏϙ = 4 ᴄᴍ.

ᴛʜᴇʀᴇғᴏʀᴇ,

ᴘϙ = ᴏᴘ + ᴏϙ

=) ᴘϙ = (3 + 4) ᴄᴍ

=) ᴘϙ = 7 ᴄᴍ.

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