Question -
Answer -
In right тИЖABC, тИаB = 90┬░
BC = 6 cm, AB = 8 cm
Let r be the radius of incircle whose centre is O and touches the sides A B, BC and CA at P, Q and R respectively
AP and AR are the tangents to the circle AP = AR
Similarly CR = CQ and BQ = BP
OP and OQ are radii of the circle
OP тКе AB and OQ тКе BC and тИаB = 90┬░ (given)
BPOQ is a square
BP = BQ = r
AR = AP = AB тАУ BD = 8 тАУ r
and CR = CQ = BC тАУ BQ = 6 тАУ r
But AC┬▓ = AB┬▓ + BC┬▓ (Pythagoras Theorem)
= (8)┬▓ + (6)┬▓ = 64 + 36 = 100 = (10)┬▓
AC = 10 cm
=> AR + CR = 10
=> 8 тАУ r + 6 тАУ r = 10
=> 14 тАУ 2r = 10
=> 2r = 14 тАУ 10 = 4
=> r = 2
Radius of the incircle = 2 cm