If AB, AC, PQ are tangents in the figure and AB = 5 cm then perimeter of  is :A 5 cm B 10 cm C 12 cm         D 15 cm

1. Break Down the Problem

We are given that AB, AC, and PQ are tangents to a circle from point A and that AB = 5 cm. We need to find the perimeter of the figure formed by these tangents.

2. Relevant Concepts

For tangent segments drawn from a common external point to a circle, we know that:

• The lengths of the tangents from the same external point to the points of tangency are equal.

3. Analysis and Detail

Let us denote the lengths of:

• AB = 5 cm (given)
• AC = 5 cm (since it is also a tangent from point A)
• PQ = the length of another tangent from point P which we need to determine.

Since it is not specified how PQ relates to the other tangents, let's assume it is another segment formed by equal tangents from another point. If we consider PQ as another pair of equal tangents from a point, its total contribution would depend on its configuration.

However, if we only consider the given lengths:

• The perimeter of the triangle formed by A, B, and C using the tangents would be: $Perimeter = AB + AC + BC$ Where BC would also equal 5 cm if drawn similarly. Therefore: $Perimeter = 5 + 5 + 5 = 15 \, \text{cm}$

4. Verify and Summarize

Based on our calculations and the properties of tangents from a common point, the perimeter calculated is valid with the dimension given in the options.

Final Answer

The perimeter of the figure is 15 cm (D).