Question

the tangent to a circle of radius 6cm from an external point p is the length of 8cm.calculate the distance of p from the nearent point of the circle​

Answer 1

Step-by-step explanation:

ʟᴇᴛ ᴘ ʙᴇ ᴛʜᴇ ᴇxᴛᴇʀɴᴀʟ ᴘᴏɪɴᴛ.

ᴏ ʙᴇ ᴛʜᴇ ᴏʀɪɢɪɴ.

ᴊᴏɪɴ ᴏ ᴀɴᴅ ᴘ ɢᴇᴛ ᴏᴘ ᴀɴᴅ ɴᴇᴀʀᴇsᴛ ᴘᴏɪɴᴛ ᴏɴ ᴛʜᴇ ᴄɪʀᴄʟᴇ ғʀᴏᴍ ᴘ ʙᴇ ᴀ.

ʟᴇᴛ ǫ ʙᴇ ᴛʜᴇ ᴘᴏɪɴᴛ ᴏɴᴛʜᴇ ᴄɪʀᴄʟᴇ ɪɴ ᴡʜɪᴄʜ, ᴛᴀɴɢᴇɴᴛ ᴍᴀᴋᴇ ° ᴡɪᴛʜ ʀᴀᴅɪᴜs ᴀᴛ ǫ.

ᴘǫ = ᴀɴᴅ ᴏǫ = ᴡᴇ ɢᴇᴛ ᴀ ʀɪɢʜᴛ ᴀɴɢʟᴇᴅ ᴛʀɪᴀɴɢʟᴇ ᴘǫᴏ ʀɪɢʜᴛ ᴀɴɢʟᴇᴅ ᴀᴛ ǫ.

sᴏ, ᴏᴘ^ = ᴏǫ^ + ᴘǫ^= ^ + ^ = + === ᴛʜᴇʀᴇғᴏʀᴇ ᴏᴘ =ᴄᴍ

ᴡᴇ ɴᴇᴇᴅ ɴᴇᴀʀᴇsᴛ ᴘᴏɪɴᴛ ғʀᴏᴍ ᴘ, ᴡʜɪᴄʜ ɪs ᴘᴀ ᴘᴀ = ᴏᴘ - ᴏᴀ= -=ᴄᴍ

Answer 2

Radius of the circle = 6 cm

Length of tangent = 8 cm

Let OP be the distance

OA = 6 cm

AP = 8 cm .

OA is the radius

OA ⊥ AP

Now In right ∆OAP,

OP² = OA² + AP²

(By Pythagoras theorem)

= (6)² + (8)²

=36 + 64

= 100

= (10)²

OP = 10 cm Ans