2015 · Q53
Let a, b, c be the sides of a right triangle, where c is the hypotenuse. The radius of the circle which touches the sides of the triangle is
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A(a+b-c)/ 2
- B(a+b+c)/ 2
- C(a+b+2c)/ 2
- D(2a+2b-c)/ 2
Explanation
Inradius r = Δ/s = (ab/2)/((a+b+c)/2) = ab/(a+b+c); using c² = a²+b² this simplifies to (a+b−c)/2 (option A).