Question

In triangle ABC is a right triangle right angled at B such that BC = 6 and AB =8 cm find the radius of its inner circle​

Answer 1

Sorry but I know only half process
first you want to find the hypotenuse

Answer 2

in ∆ABC, we have

∠B=90° , AB=6cm and BC = 8cm

we know, as Circle is inscribed in a triangle

OM⊥AB, ON⊥BC, OP⊥CA

Let r cm be the radius of the circle.

Then,

OM=ON=OP=r cm.

Now,

AB²+BC²=CA² [by Pythagoras Theorem]

=> 6² + 8² = CA²

=> CA= 10cm

Now,

area(∆ABC)=area(∆AOB)+area(∆BOC)+(∆COA)

=> ½ × AB × BC = (½× AB × OM)+(½×BC×ON)+(½×CA×OP)

=> ½×6×8= (½×6×r)+(½×8×r)+(½×10×r)

=> r=2

∴Radius=2cm

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