Question 1 (a) Two circles of radii $5 \mathrm{~cm}$ and $8 \mathrm{~cm}$ touch each other externally. Calculate the length of the common tangent.

Step 1 ：Given two circles of radii \(5 \mathrm{~cm}\) and \(8 \mathrm{~cm}\) that touch each other externally, we are to calculate the length of the common tangent.

Step 2 ：The length of the common tangent between two circles that touch each other externally can be calculated using the formula: \[\sqrt{(r2 - r1)^2}\] where \(r1\) is the radius of the smaller circle and \(r2\) is the radius of the larger circle.

Step 3 ：Substituting the given values into the formula, we get: \[\sqrt{(8 - 5)^2} = \sqrt{9} = 3\]

Step 4 ：Final Answer: The length of the common tangent between the two circles is \(\boxed{3}\) cm.