Question

${\textbf{Subject : Mathematics}}$

${\textbf{Chapter : Tangency}}$


A point P is 16 cm from the centre of the circle. The length of tangent drawn from P to the circle is 12 cm. Find the radius of the circle.​

Answer 1

Hey !

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ɢɪᴠᴇɴ : ᴘ ɪs ᴀ ᴘᴏɪɴᴛ ᴀᴛ ᴅɪsᴛᴀɴᴄᴇ ᴏғ 16ᴄᴍ ғʀᴏᴍ ᴛʜᴇ ᴄᴇɴᴛʀᴇ ᴏғ ᴀ ᴄɪʀᴄʟᴇ ᴏ. ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏғ ᴛᴀɴɢᴇɴᴛ ᴅʀᴀᴡɴ ғʀᴏᴍ ᴘ ᴛᴏ ᴛʜᴇ ᴄɪʀᴄʟᴇ ɪs 12 ᴄᴍ.

ɪᴛ ɪs ʀᴇǫᴜɪʀᴇᴅ ᴛᴏ ᴍᴇᴀsᴜʀᴇ ᴛʜᴇ ʀᴀᴅɪᴜs ᴏғ ᴛʜᴇ ᴄɪʀᴄʟᴇ.

ɴᴏᴡ, ∠ᴏᴛᴘ= 90°

( ∵ ᴀ ᴛᴀɴɢᴇɴᴛ ᴛᴏ ᴀ ᴄɪʀᴄʟᴇ ɪs ⊥ ᴛᴏ ᴛʜᴇ ʀᴀᴅɪᴜs ᴛʜʀᴏᴜɢʜ ᴛʜᴇ ᴘᴏɪɴᴛ ᴏғ ᴄᴏɴᴛᴀᴄᴛ).

∴ ɪɴ ʀɪɢʜᴛ ᴀɴɢʟᴇ ᴛʀɪᴀɴɢʟᴇ ᴏᴛᴘ,

ᴏᴘ² = ᴏᴛ²+ ᴛᴘ²

ᴏʀ, 16² = ᴏᴛ² + (12)²

ᴏʀ, 256-144 = ᴏᴛ²

ᴏʀ, 112 = ᴏᴛ²

∴ ᴏᴛ = 10.89 ᴄᴍ

ʜᴇɴᴄᴇ, ʀᴀᴅɪᴜs = 10.89 ᴄᴍ

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Thanks !

Answer 2

Explanation:

1) After the Civil Disobedience Movement was brutally supressed by the British, the Gandhi-Irwin pact was signed. According to this pact, if Gandhi agreed to attend the next round table conference, Irwin was willing to release the political prisoners except those who were violent. Gandhi agreed to this. However, the negotiations broke down and by the time Gandhi came back to India, most of the political leaders were arrested. Women and children were also attacked and brutally suppressed.

2)WBC - White Blood Cells1) After the Civil Disobedience Movement was brutally supressed by the British, the Gandhi-Irwin pact was signed. According to this pact, if Gandhi agreed to attend the next round table conference, Irwin was willing to release the political prisoners except those who were violent. Gandhi agreed to this. However, the negotiations broke down and by the time Gandhi came back to India, most of the political leaders were arrested. Women and children were also attacked and brutally suppressed.

2)WBC - White Blood Cells