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Circles
NCERT Exemplar
CBSE
Grade 10

Question:

If a tangent $PQ$ at a point $P$ of a circle of radius $5\text{ cm}$ meets a line through the center $O$ at a point $Q$ so that $OQ = 12\text{ cm}$, then length $PQ$ is:
(a) $12\text{ cm}$
(b) $13\text{ cm}$
(c) $8.5\text{ cm}$
(d) $\sqrt{119}\text{ cm}$

Step-by-Step Solution

Key Concept: $OP \perp PQ$. In right $\Delta OPQ$, $PQ = \sqrt{OQ^2 - OP^2}$.
$PQ = \sqrt{12^2 - 5^2} = \sqrt{144 - 25} = \sqrt{119}\text{ cm}$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Pythagoras formula evaluation $\sqrt{12^2 - 5^2} = \sqrt{119}\text{ cm}$: 1.0 Mark

Correct Answer: $\sqrt{119}\text{ cm}$
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