Question:
In a circle of radius 7 cm, tangent PT is drawn from a point P, such that PT = 24 cm. If O is the centre of the circle, then OP = ?
(a) 30 cm
(b) 28 cm
(c) 25 cm
(d) 18 cm
Solution:
(c) 25 cm
The tangent at any point of a circle is perpendicular to the radius at the point of contact.
$\therefore O T \perp P T$
From right $-$ angled triangle $P T O$,
$\therefore O P^{2}=O T^{2}+P T^{2}[$ Using Pythagoras' theorem $]$
$\Rightarrow O P^{2}=(7)^{2}+(24)^{2}$
$\Rightarrow O P^{2}=49+576$
$\Rightarrow O P^{2}=625$
$\Rightarrow O P=\sqrt{625}$
$\Rightarrow O P=25 \mathrm{~cm}$
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