Question

1. find the perimeter of \\( \triangle pqr \\).

Explanation:

Step1: Use the property of tangents

From a point outside a circle, the lengths of the two tangent segments to the circle are equal.
Let the lengths of the tangent segments be \(x\), \(y\), \(z\) as follows:
Let the tangent from \(P\) to the circle be \(x\), from \(Q\) be \(y\), and from \(R\) be \(z\).
We know that \(x + y=27.4\), \(y + z = 5.9\), \(x+z = 12.2\)
The perimeter \(P\) of \(\triangle PQR=(x + y)+(y + z)+(x + z)\)

Step2: Calculate the perimeter

$$
LATEXBLOCK0
$$

Substitute \(x + y = 27.4\), \(y + z=5.9\), \(x + z = 12.2\) into the above formula:

$$
LATEXBLOCK1
$$

Answer:

\(45.5\)