# Find the length of PA - deductive Geometry

• chwala
In summary, deductive geometry is a branch of mathematics that uses logical reasoning and a set of axioms to prove geometric theorems. The length of PA is determined using the principles of deductive geometry, which involve using previously proven theorems and axioms to logically deduce the length of the line segment PA. The steps involved in finding the length of PA include identifying the given information, using known geometric principles and theorems to make deductions, and using algebraic equations to solve for the length of PA. While the length of PA can also be found using other methods such as coordinate geometry or trigonometry, deductive geometry provides a more systematic and logical approach. In deductive geometry, a solution for the length of PA

#### chwala

Gold Member
Homework Statement
see attached
Relevant Equations
Geometry
Text question is here and solution;

My approach;
##BP ×AP= PT^2##
Let ##AP= x##
Therefore, ##(6+x)x=16##
##x^2+6x-16=0##
##x=2## or##x=-8##
##⇒x=2## positive value only.

I guess this may be the only approach. Cheers!

## 1. What is deductive geometry?

Deductive geometry is a branch of mathematics that uses logical reasoning and deductive reasoning to prove theorems and solve geometric problems.

## 2. How do you find the length of PA in deductive geometry?

To find the length of PA in deductive geometry, you will need to use the Pythagorean theorem or other geometric theorems to calculate the length. This will involve using given information and applying geometric principles to solve for the unknown length.

## 3. What information do I need to know to find the length of PA in deductive geometry?

You will need to know the coordinates or measurements of other points or lines in the geometric figure, as well as any given angles or lengths. It is also helpful to have a good understanding of geometric principles and theorems.

## 4. Can I use any method to find the length of PA in deductive geometry?

Yes, there are multiple methods that can be used to find the length of PA in deductive geometry, such as using the Pythagorean theorem, the distance formula, or other geometric theorems. The method you choose will depend on the given information and the specific problem you are trying to solve.

## 5. Why is finding the length of PA important in deductive geometry?

Finding the length of PA is important in deductive geometry because it allows us to solve geometric problems and prove theorems. It also helps us understand the relationships between different points and lines in a geometric figure, which is crucial in many real-world applications such as architecture, engineering, and navigation.