# Basic triangle plane geometry problem - impossible?

• rieuk
In summary, a basic triangle plane geometry problem involves using geometric principles and formulas to find missing measurements of a triangle. These problems may be considered impossible if there is not enough information given or if the information contradicts known principles. Common techniques for solving these problems include using the Pythagorean theorem, properties of similar triangles, and trigonometric functions. If encountering an impossible problem, one should carefully review the given information and seek help if needed. While some impossible problems can be solved with creative thinking, there may be cases where a solution is not possible due to insufficient or contradictory information.
rieuk
Consider a point P inside a triangle ABC. Angle PBC is 10 degrees, angle PCB is 20 degrees, and angle BAC is 100 degrees. Find angle PAC.

Question is that is this problem even solvable? I found it in an Olympiad training book...

hi rieuk!

no, A could be anywhere on an arc of a circle, so PAC could be anything between 0° and 100°

That's what I thought! Cheers!

## What is a basic triangle plane geometry problem?

A basic triangle plane geometry problem involves finding missing angles, sides, or other measurements of a triangle using geometric principles and formulas.

## Why is the problem considered impossible?

The problem is considered impossible because it may not have enough information given to solve it, or the given information may contradict the known principles of geometry.

## What are some common techniques used to solve this type of problem?

Some common techniques include using the Pythagorean theorem, the properties of similar triangles, or trigonometric functions such as sine, cosine, and tangent.

## What should I do if I encounter an impossible triangle plane geometry problem?

If you encounter an impossible problem, you should carefully review the given information and try different approaches to see if you can find a solution. If you are still unable to solve it, you may need to ask for help from a teacher or tutor.

## Can impossible triangle plane geometry problems be solved?

In some cases, with careful analysis and creative thinking, impossible problems can be solved. However, there may be cases where the problem is truly impossible to solve due to insufficient or contradictory information.

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