Question

the length of a tangent from a point a at distance 5 cm from the centre of the circle is 4 cm find the radius of a circle​

Answer 1

Hᴇʀᴇ's Yᴏᴜʀ Aɴsᴡᴇʀ:-

AB ɪs ᴀ Tᴀɴɢᴇɴᴛ Dʀᴀᴡɴ ᴏɴ Tʜɪs Cɪʀᴄʟᴇ Fʀᴏᴍ Pᴏɪɴᴛ A.

. ° . OB ⍊ AB

OA = 5cm Aɴᴅ AB = 4cm ( Gɪᴠᴇɴ )

Iɴ △ABO,

Bʏ Pʏᴛʜᴀɢᴏʀᴀs Tʜᴇᴏʀᴀᴍ ɪɴ △ABO,

OA2 = AB2 + BO2

⇏52 = 42 + BO2

⇏BO2 = 25 - 16

⇏BO2 = 9

⇏BO = 3

Tʜᴇ Rᴀᴅɪᴜs ᴏғ Tʜᴇ Cɪʀᴄʟᴇ ɪs 3 ᴄᴍ.

Hᴏᴘᴇ ɪᴛ Hᴇʟᴘs ᴜʜ......

Hᴀᴠᴇ ᴀ Gʀᴇᴀᴛ Dᴀʏ......

Answer 2

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$\bf\underbrace{Question:}$

• The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.??

$\bf\underline{Given:}$

• Let the circle be with centre O
• AB is the tangent from point A
• Length of tangent = AB = 4cm
• Also, distance of point from circle = 5 cm

Hence OA = 5cm

$\bf\underline{To\:Find:-}$

• Radius i.e. OB

$\bf\underbrace\orange{Solution:}$

• $\sf{ Since\:AB\:is\: tangent}$
• $\sf{Hence \:OB\: || AB}$
• ∴ $\sf{∠OAB = 90°}$

So,

A OAB is a right triangle

In right triangle OAB

Using Pythagoras theorem

(Hypotenuse)² = (Height)² + (Base)²

ㅤㅤ$⟹$$\sf\red{OA² = OB² + AB²}$

ㅤㅤ$⟹$$\sf\red{5² = OB² + 4²}$

ㅤㅤ$⟹$$\sf\red{OB² = 25 - 16}$

ㅤㅤ$⟹$$\sf\red{OB² = 9}$

ㅤㅤ$⟹$$\sf\red{OB = }$$\sf\red{ \sqrt{9}}$

ㅤㅤ$⟹$$\sf\red{OB = }$$\sf\red{ \sqrt{3²}}$

ㅤㅤ$⟹$$\sf\red{OB = 3}$

$\text{\large\underline{\purple{Hence,}}}$

$\sf\underline{ Radius \:of\: the\: circle \:= OB = \:3cm}$

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