ABC is a right triangle in which angle B = 90°. The biggest circle possible is inscribed in the triangle. If AB = 8 cm and BC = 6 m, find the radius r of the incircle.

Area of right ^$\triangle$ABC = 1/2 x AB x BC= 1/2 x (6 x 8)cm² = 24 cm²     AC² = AB² + BC²                             64 cm² + 36 cm² = 100 cm². AC = 10 cm.  Also, area (^$\triangle$ABC) = ar (^$\triangle$OBC) + ar (^$\triangle$OCA) + ar (^$\triangle$OAB)= 1/2 (BC x r) + 1/2 (AC x r) + 1/2 (AB x r)= 1/2 r (6 + 10 +8) cm = 12 r cm 12 r cm = 24 cm^{2 _{$\Rightarrow$}} r = 2 cm