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From an external point $P$, a tangent $PT$ is drawn to a circle. A secant $PAB$ passes through the circle such that $PA = 9$ cm and $AB = 7$ cm. Find the length of the tangent $PT$.

1. 10 cm
2. 12 cm
3. 14 cm
4. 16 cm

Correct answer: 12 cm

Solution

For a tangent and secant from the same external point, $PT^2 = PA \cdot PB$. Here $PB = PA + AB = 9 + 7 = 16$ cm, so $PT^2 = 9 \times 16 = 144$. Therefore, $PT = 12$ cm.

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