Question

Find the length of the tangent
point 13 cm away from the centre of
the circle of radius 5 cm​

Answer 1

ᴡᴇ ʜᴀᴠᴇ ᴛᴏ ғɪɴᴅ ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏғ ᴛᴀɴɢᴇɴᴛ ᴅʀᴀᴡɴ ғʀᴏᴍ ᴀ ᴘᴏɪɴᴛ 13ᴄᴍ ᴀᴡᴀʏ ғʀᴏᴍ ᴛʜᴇ ᴄᴇɴᴛʀᴇ ᴏғ ᴀ ᴄɪʀᴄʟᴇ ᴏғ ʀᴀᴅɪᴜs 12ᴄᴍ.

ʟᴇᴛ ᴛᴀɴɢᴇɴᴛ ɪs ᴅʀᴀᴡɴ ғʀᴏᴍ ᴘ ᴡʜɪᴄʜ ᴛᴏᴜᴄʜᴇs ᴛʜᴇ ᴄɪʀᴄʟᴇ ᴀᴛ ᴛ. ᴇ.ɢ., ʟᴇɴɢᴛʜ ᴏғ ᴛᴀɴɢᴇɴᴛ ɪs ᴘᴛ ᴀɴᴅ ᴄᴇɴᴛʀᴇ ᴏғ ᴄɪʀᴄʟᴇ ɪs ᴏ.

ɢɪᴠᴇɴ, ᴘᴏ = 13ᴄᴍ , ᴏᴛ = ʀᴀᴅɪᴜs = 12ᴄᴍ

ᴡᴇ ᴋɴᴏᴡ, ᴛᴀɴɢᴇɴᴛ ɪs ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ ᴜᴘᴏɴ ʀᴀᴅɪᴜs ᴏғ ᴄɪʀᴄʟᴇ sᴏ, ∆ᴘᴏᴛ ɪs ʀɪɢʜᴛ ᴀɴɢʟᴇᴅ ᴛʀɪᴀɴɢʟᴇ.

sᴏ, ᴘᴛ² + ᴏᴛ² = ᴏᴘ²

ᴘᴛ² + 12² = 13²

ᴘᴛ² = 169 - 144 = 25

ᴘᴛ = 5ᴄᴍ

ʜᴇɴᴄᴇ, ʟᴇɴɢᴛʜ ᴏғ ᴛᴀɴɢᴇɴᴛ = 5ᴄᴍ

Answer 2

Step-by-step explanation:

we have to find the length of tangent drawn from a point 13cm away from the centre of a circle of radius 12cm.

Let tangent is drawn from P which touches the circle at T. e.g., length of tangent is PT and centre of circle is O.

Given, PO = 13cm , OT = radius = 12cm

we know, tangent is perpendicular upon radius of circle so, ∆POT is right angled triangle.

so, PT² + OT² = OP²

PT² + 12² = 13²

PT² = 169 - 144 = 25

PT = 5cm

hence, length of tangent = 5cm