Question

ABC is a triangle right angled at B such that BC = 6cm, AB = 8 cm. A circle with center O is inscribed inside the triangle. OP⊥AB, OQ⊥BC and OR⊥AC. If OP = OQ = OR = x, then x is equal to​

Answer 1

Step-by-step explanation:

Let ABC be the right angled triangle such that ∠B = 90° , BC = 6 cm, AB = 8 cm. Let O be the centre and r be the radius of the in circle.

AB, BC and CA are tangents to the circle at P, N and M.

∴ OP = ON = OM = r (radius of the circle)

By Pythagoras theorem,

 CA2 = AB2 + BC2

 ⇒ CA2 = 82 + 62

⇒ CA2 = 100

⇒ CA = 10 cm

Area of ∆ABC = Area ∆OAB + Area ∆OBC + Area ∆OCA