Search 7,000+ topics

Inradius of Right Triangle

Before this, knowIn-Touch Triangle and Length-Finding

PracticeHarder problems from real math contests

Illustrated · 1 min

By Michael Li
+1 contributors
Contributors

Example: Inradius of right triangle

Right triangle with the right angle at C, legs a (BC) and b (CA), and hypotenuse c (AB). A circle centered at I touches all three sides, with radii meeting each side at right angles.

Given the above right triangle, the inradius is denoted by a dotted red line.

Inradius r can be solved using the following equation:

r = 12\frac{1}{2} (a + b - c)

Furthermore, we know that (a + b - c) must be an even positive integer. Therefore, the inradius must be a positive integer.

References:

Art of Problem Solving

math.stackexchange

Find your level

The problems run from approachable to very hard, and each is rated by how often real students solve it, so you can pick your next step. These are real problems from the AMC 12 and AIME, the national math competitions for middle and high school students, each with a worked solution on LIVE by Po-Shen Loh.

Keep going

Type a concept, like “slope” or “photosynthesis”.

↑ ↓ to choose · Enter to openSearch explanations and problems