Right triangle
Inequalities

In any right triangle the diameter of the incircle is less than half the hypotenuse, and more strongly it is less than or equal to the hypotenuse times (2 − 1). {\displaystyle ({\sqrt {2}}-1).}

In a right triangle with legs a, b {\displaystyle a,b} and hypotenuse c, {\displaystyle c,}

with equality only in the isosceles case.

If the altitude from the hypotenuse is denoted h c, {\displaystyle h_{c},} then

with equality only in the isosceles case.
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