In the given figure, $P T$ is a tangent to the circle. If $P A = 5 c m$ and $P T = 10 c m,$ then the radius of the circle is ___ $c m .$

4 cm

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2 cm

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6 cm

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3 cm

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Solution

The correct option is C: $7.5 c m$

Given: $P A = 5 c m, P T = 10 c m$
Let Radius $= O T = O A = x c m$

Using Pythagoras theorem, we have
$O P^{2} = O T^{2} + T P^{2}$
$\Rightarrow (O A + P A)^{2} = x^{2} + 10^{2}$
$\Rightarrow (x + 5)^{2} = x^{2} + 100$
$\Rightarrow x^{2} + 25 + 10 x = x^{2} + 100$
$\Rightarrow 10 x = 75$
$∴ x = 7.5 c m$
Hence, the radius of the given circle is $7.5 c m$

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In the given figure, PT is a tangent to the circle. If PA=5 cm and PT=10 cm, then the radius of the circle is ___ cm.

The correct option is C: 7.5 cmGiven: PA=5 cm,PT=10 cmLet Radius =OT=OA=x cm Using Pythagoras theorem, we haveOP2=OT2+TP2⇒(OA+PA)2=x2+102⇒(x+5)2=x2+100⇒x2+25+10x=x2+100⇒10x=75∴x=7.5 cmHence, the radius of the given circle is 7.5 cm

In the given figure, $P T$ is a tangent to the circle. If $P A = 5 c m$ and $P T = 10 c m,$ then the radius of the circle is ___ $c m .$