Question

The length of the tangent from a point 61cms away from the centre of a circle is 60cms what is the radius of the circle
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Answer 1

Answer:

Step-by-step explanation:

Let AB be a tangent drawn from B to a circle with centre O such that AB = 60 cm and OB = 61 cm.

In right angled △ OAB,

OB^2 = OA^2 + AB^2

 61^2 = OA^2 + 60^2

OA^2 =  61^2 -  60^2

OA^2 =  3721 -  3600

OA^2 = 121

   OA =  $\sqrt{121}$

   OA= 11 cm

Hence, the radius of circle is 11 cm.

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Answer 2

Given: The length of the tangent from a point 61cms away from the centre of a circle is 60cms.

To find: the radius of the circle.

Solution:

Assume that AB is a tangent drawn from B to a circle with centre O such that $AB = 60$cm and $OB = 61$ cm.

Understand that, In right-angled $\[\Delta OAB,\]$

$\[\begin{array}{l}O{B^2} = O{A^2} + A{B^2}\\ \Rightarrow {61^2} = O{A^2} + {60^2}\\ \Rightarrow O{A^2} = {61^2} - {60^2}\\ \Rightarrow O{A^2} = 3721 - 3600\end{array}\]$

$\[\begin{array}{l} \Rightarrow O{A^2} = 121\\ \Rightarrow OA = 11cm\end{array}\]$

Hence, the radius of circle is $11 cm$.