A circle is inscribed within a right triangle. Considering that the lengths of the two legs measure 6 cm and 8 cm, what is the radius of the inscribed circle?
A. 2 cm (Correct answer)
B. 3 cm
C. 4 cm
D. 5 cm
Correct Answer
Option A — 2 cm
Detailed Solution & Explanation
The correct answer is 2 cm.
Key Points
For a right triangle, the inradius is r = (a + b − c)/2, where a and b are the legs and c the hypotenuse.
Here c = √(6² + 8²) = √100 = 10, so r = (6 + 8 − 10)/2 = 4/2 = 2 cm.
This compact formula (from the general r = Area/semi-perimeter, which simplifies for right triangles) saves you from constructing tangent lengths.