Question

In the figure, point A is the centre of the
circle. AN=10 cm. Line NM is tangent at M. Determine the radius of the circle, if MN = 5cm.​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given: A is centre of circle . AN =10 cm .. NM is tangent at M and MN= 5cm

To find: Radius of circle

Step-by-step explanation:

As given

A is centre of circle and NM is the tangent at M

Now as we know  

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

Therefore

∠AMN = 90°

Therefore  Δ AMN is a right angle triangle

So by Pythagoras theorem which states that : In a right angle triangle  square of the hypotenuse side is equal to the sum of squares of other two sides

Therefore

$H^2=P^2+B^2$ where H is hypotenuse , P and B are the other two sides

$AN^2= MN^2+AM^2\\\\\Rightarrow 10^2= 5^2+AM^2\\\\\Rightarrow 100 = 25+AM^2\\\\\Rightarrow AM^2= 100-25=75\\\\\Rightarrow AM=\sqrt{75}= 5\sqrt{3}$

Hence the radius of the circle is 5√3 cm