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Tangent Secant Segments Theorem

In the given ...

Question

In the given figure, PS is a tangent and line PR is a secant to the circle. If PQ = 4.9 cm and QR = 5.1 cm, then find PS. [2 Marks]

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Solution

$P S^{2} = P Q \times P R$ ...(Tangent secant segments theorem)
$P S^{2} = P Q \times (P Q + Q R)$ [1 Mark]
= 4.9 (4.9 + 5.1)
= 4.9 $\times$ 10 = 49
$∴ P S = 7 c m$ [1 Mark]

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P Q = 3.6

Q R = 6.4

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: {P S}^{2} = P Q \times P R \dots

\begin{matrix} = P Q \times (P Q + Q R) = 3.6 \times [3.6 + 6.4] = 3.6 \times 10 = 36 ∴ P S & = 6 \end{matrix}

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