Question

1. find pq. 14x - 13 8x + 5

Explanation:

Step1: Use the tangent - segment theorem

Tangents from the same external point to a circle are equal. So, \(QP = QR\).
$$14x - 13=8x + 5$$

Step2: Solve the equation for \(x\)

Subtract \(8x\) from both sides:
$$14x-8x - 13=8x-8x + 5$$
$$6x-13 = 5$$
Add \(13\) to both sides:
$$6x-13 + 13=5 + 13$$
$$6x=18$$
Divide both sides by \(6\):
$$x=\frac{18}{6}=3$$

Step3: Find the length of \(PQ\)

Substitute \(x = 3\) into the expression for \(PQ\) (\(PQ=14x - 13\))
$$PQ=14\times3-13$$
$$PQ = 42-13$$
$$PQ=29$$

Answer:

\(29\)