Sometimes the simplest thing to do is start doing things that you know how to do, simply because you know how to do them. For example, given a geometric problem like the first thing to do is draw a diagram.Find the radius of a circle inscribed in an isosceles triangle with sides 12, 12, and 8.
But what then? Well, any time you see a triangle, you should probably be reminded of the Pythagorean Theorem. So you might look for ways to apply it to the diagram.
To use it, you need to have a right triangle.
You don't have one, but you
Or you might try placing a point at the center of the circle, and drawing line segments from there to the vertices of the triangle. Now you have four triangles instead of one. Can you identify any of the angles? Can you determine which angles are equal to others?
After looking at that for a while, you might try drawing more segments from the center, this time to the points where the circle touches the sides of the triangle. What can you say about those segments? One thing you can say is that each of them has the same length as the radius of the circle... which is what you're looking for!
It's important to realize that not everything you try will move you closer to a solution. What's important is that just about anything you try will generate more information than you have right now, and often just looking at that information will suggest new directions for you to move in. |