Ex.10.2 Q6 Circles Solution - NCERT Maths Class 10

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Question

The length of a tangent from a point \(A\) at distance \(\text{5 cm}\) from the center of the circle is \(\text{4 cm.}\) Find the radius of the circle.

Text Solution

 

What is Known?

Length of tangent from point \(A = \text{4 cm.}\)

Distance between the centre of the circle and point \(A\) is \(\text{5 cm.}\)

What is Unknown?

Radius of the circle

Reasoning:

Tangent at any point of a circle is perpendicular to the radius through the point of contact.

Therefore, \(\angle {OTA} = {90^ \circ }\) and \(\Delta {OTA}\) is right angled triangle.

Steps:

By Pythagoras theorem

\[\begin{align} {O A} ^ { 2 } &= {O T} ^ { 2 } + {A T} ^ { 2 } & \\ 5 ^ { 2 } & = {O T} ^ { 2 } + 4 ^ { 2 } \\ {O T} ^ { 2 } & = 25 - 16 \\ {O T} ^ { 2 } & = 9 \\ {O T} & = \pm 3 \end{align}\]

Radius \(OT\) cannot be negative. Hence, the radius is \(\text{3 cm.}\)

  
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