In the diagram shown below, a circle just touches the sides of a right triangle whose sides are 5 units, 12 units and 13 units.

Question

Draw in radius lines and find the radius of the circle in this 5, 12, 13 right triangle. Explain your work and show your calculations.

Answer 1

Hi Luna A.,

The phrase you should have used is "inscribed in a right triangle..."

The problem is clear.

So what do you have? The initial right triangle, and (once you have drawn the radii as perpendiculars to each of the initial triangle sides, and also segments from the circle center to each of the initial triangle's vertices) three pairs of identical triangles. You should then be able to use the Pythagorean theorem to establish some algebraic equalities involving the side lengths of the little triangles. At most, you might need to introduce one side of a little triangle as a variable (all the other sides are related to that algebraically!), and solve for that variable, using the fact that the six little triangles sum to the big area. So there are many ways to wring information out of the figure. This should get you started calculating, anyway?

-- Cheers, --Mr. d.